Saying Baruch Hamavdil or Havdala prior to doing Melacha:
Even after the time of night that hails the leave of Shabbos has arrived the Sages forbade one from doing Melacha until he escorts the King. This is done through reciting Havdala in prayer or over wine, or through simply saying the words “Baruch Hamavdil Bein Kodesh Lechol”.
Performing Rabbinical prohibitions prior to saying Hamavdil: The above prohibition of doing Melacha prior to saying Hamavdil applies likewise to Rabbinical Melacha. Thus one may not even move the Havdala candle until he says Havdala in prayer or says Baruch Hamavdil. (However those Rabbinical prohibitions relevant to speech are permitted even before saying Havdala or Baruch Hamavdil, once Shabbos is over. This however is with exception to asking bodily requests from G-d which is only allowed after one says Hamavdil.) Likewise some permit performing, after Shabbos is over but prior to saying Havdala, all Rabbinical prohibitions which are forbidden simply due to them being a mundane act. Practically the custom is to be lenient on Motzei Yom Kippur. [According to this opinion one may measure an item once Shabbos is over, even prior to reciting Baruch Hamavdil.]
Performing Melacha prior to Havdala over wine: After Havdala has been recited within prayer, or one has recited the words “Baruch Hamavdil Bein Kodesh Lechol, he may perform all forms of Melacha even prior to saying Havdala over wine. [See next Halacha regarding doing Melacha prior to Maariv or prior to Havdala or prior to eating Melaveh Malka.]
Reminding women to say Baruch Hamavdil:  It is of importance to remind women to say Baruch Hamavdil immediately after Shabbos, prior to doing any Melacha. One is to mention this obligation in public gatherings. Those women who do time consuming Melacha prior to saying Baruch Hamavdil are to be protested. Those women who Daven Maariv on Motzei Shabbos are to say Havdala in Ata Chonantanu just like men. They are not required to say Baruch Hamavdil after Davening Maariv unless they forget to say it in Maariv.
Hearing Baruch Hamavdil from another person: Those which do not know to say Baruch Hamavdil are to hear another person say it [and intend to fulfill their obligation through hearing it].
On Motzei Shabbos which is Yom Tov: Based on the above when Yom Tov falls on Motzei Shabbos one may not begin doing any Melacha which is permitted on Yom Tov until he says Havdala, or recites Baruch Hamavdil Bein Kodesh Lekodesh, after the conclusion of Shabbos. It is of importance to remind women of this requirement, and have them say Baruch Hamavdil prior to doing any Yom Tov preparations.
Does one fulfill his obligation if he thought the words of “Baruch Hamavdil” without verbalizing them?
No. However there are Poskim which write that doing so is valid.
If one is in the bathroom by the leave of Shabbos and needs to cut toilet paper may he say “Baruch Hamavdil” in that area?
Some write one is to think the words of Baruch Hamavdil in his head and then tear the paper with an irregularity if possible.
If a woman lit Yom Tov candles on the second night of Yom Tov and after saying the blessing remembered that she did not yet say Baruch Hamavdil, what is she to do?
Some write she is to think the words in her mind and then light one candle, and then verbalize the Baruch Hamavdil. Afterwards she may light the other candles.
If one recited “Baruch Hamavdil Bein Kodesh Lechol” instead of “Bein Kodesh Lekodesh” on Motzei Shabbos which is Yom Tov has he fulfilled his obligation?
Some rule that he has fulfilled his obligation, although seemingly he should repeat the correct Nusach.
If a Jew did Melacha prior to saying Baruch Hamavdil, may another Jew benefit from that Melacha?
Yes. There is no prohibition of benefiting from such Melacha being that Shabbos was already over. For this reason it is permitted to enter a bus driven by a Jew which has not said Baruch Hamavdil.
 Meaning even if three consecutive small stars are visible and it is thus no longer Shabbos, and he has already added Mechol Al Hakodesh, he may nevertheless still not do Melacha. [ibid]
 Thus the reason behind this prohibition has nothing to do with the Kedusha of Shabbos, but due to it being forbidden for one to do his own matters prior to escorting the king. This follows the ruling of the Taz 263/3
Vetzaruch Iyun why this is not forbidden due to Tosefes Shabbos in which case one cannot do any Melacha until he concludes Shabbos? Seemingly one must say that that as soon as one does Melacha after Shabbos, that itself is an action which says “my Tosefes Shabbos has concluded” and hence only due to this new prohibition of escorting the king is it forbidden to do Melacha. [See also Kitzur Halachos Miluim p. 123 for a similar explanation; Piskeiy Teshuvos 299 footnote 103; See also Other Opinions below.]
Other Opinions: The M”B [299/33] rules one must say Havdala prior to doing Melacha because the holiness of Shabbos partially continues until Havdala and therefore the Sages forbade it in Melacha. This follows the ruling of the Levush 263. The Ashel Avraham Butchatcher 299 seems to learn that the prohibition applies due to Tosefes Shabbos.
 This ruling of Admur follows the ruling of Levush. The Michaber however rules one simply says Hamavdil Bein Kodesh Lechol, without the word Baruch.
 299/16; These words serve as recognition of escorting the king. [ibid]
Other Opinions: The above wording follows the opinion of Rashi and the Beis Yosef which argue there is no need to say Hashem’s name in the blessing. Others however rule one must say Baruch Hamavdil with Hashem’s name. Practically the ruling is that one may not do so. [Kaf Hachaim 299/56] The Kitzur SH”A 96/5 based on Abudarham writes that one is to recite the entire Nusach of the blessing of Havdala recited over wine without Hashem’s name. This is not the accepted ruling of Achronim.
Gutt Voch/G-d of Avraham: See Piskeiy Teshuvos 299/16 regarding if saying Shavua Tov or G-d of Avraham is considered as if one said Baruch Hamavdil.
 Such as talking of business related matters or Amira Lenachri. [Piskeiy Teshuvos 299/13]
 Requesting bodily matters is forbidden on Shabbos, and this prohibition extends until Havdala is said. [Ibid; 294/1; Kaf Hachaim 299/51]
 With regards to blowing the Shofar after Neila. [623/11]
Other Opinions brought in Admur: There are those opinions [Rabbeinu Yerucham] which rule that only those Melachas which are time consuming and take effort, such as weaving, writing and chopping wood, were forbidden by the Sages before saying Havdala or Baruch Hamavdil. However those Melachas which are performed without any effort, such as lighting a candle or carrying 4 Amos in a public domain, are permitted even if they are of Biblical nature, if the proper time of night has arrived, even if one has not yet said Hamavdil.
Practically however Admur rules [in parentheses, and so is the main opinion-See Kaf Hachaim 299/52] that the above differentiation was only said as a stringency regarding doing Melacha after saying Havdala in prayer but prior to Havdala over wine. As some opinions [Rambam/Rosh] rule that even if one said Havdala in prayer he may still not do any time consuming Melacha until after he says Havdala over wine. However before Baruch Hamavdil or Baruch Hamavdil Havdala in prayer, no Melacha at all may be done. Thus the above differentiation was only given for those which follow this opinion. [In other words there are two disputes: 1. Can non-time consuming Melacha be done before saying Hamavdil? 2. Even if one rules non-time consuming Melacha can be done some opinions rule this is only prior to Havdala over wine and not prior to saying Hamavdil. Meaning they are even further stringent to still forbid time consuming Melacha until after Havdala over wine.]
Practically the main opinion follows that even non-time consuming Melachas are forbidden prior to Havdala or Baruch Hamavdil [unlike Rabbeinu Yerucham], and once Baruch Hamavdil has been said, all Melachos are permitted even prior to Havdala over wine [unlike the opinions which hold time consuming Melacha may not be done prior to Havdala over wine]. Nevertheless one may rely on the first opinion [Rabbeinu Yerucham] regarding not protesting women who are lenient to do non-time consuming Melachas prior to saying Baruch Hamavdil. If however they do time consuming Melachas they must be protested. [299/18]
 306/18 as measuring is only forbidden due to Uvdin Dechol.
 See previous footnote that some opinions forbid time consuming Melacha until Havdala is said over wine.
Other opinions: Some rule one may not do Melacha until he says Baruch Hamavdil even if he said Havdala in prayer. They also rule it is best to be stringent not to do any Melacha until Havdala over wine. [Chesed Leavraham brought in Kaf Hachaim 299/59; Ben Ish Chaiy Vayeitzei 22]
 See previous footnotes regarding the difference between time consuming Melacha and Melachas that can be performed without delay.
 Piskeiy Teshuvos 299 footnote 101, Upashut!
 Other Opinions: The Elya Raba rules it does not suffice on Motzei Shabbos which is Yom Tov to simply say Baruch Hamavdil Bein Kodesh Lekodesh. Rather one must say the entire blessing of Hamavdil without Sheim Umalchus. [Brought in Kaf Hachaim 299/58]
 Admur 299/15 writes “to say” Baruch Hamavdil.
 Ashel Avraham Butchacher 299 writes that if one thinks the words of Baruch Hamavdil he ends his Tosefes Shabbos [and can then do Melacha. See Piskeiy Teshuvos 299 footnote 101.
 See Piskeiy Teshuvos 299 footnote 101
 Sheivet Hakehasy 6/153
 Piskeiy Teshuvos 299 footnote 102
 Based on M”A 299/9 that one who says Bein Kodesh Lekodesh when he is meant to say Bein Kodesh Lechol is saying a lie.
 Piskeiy Teshuvos 299/13; Tzitz Eliezer 11/34
In the case of one who is in the bathroom at the time that Shabbos ends, and he desires to tear toilet paper – practically speaking, one is allowed to tear toilet paper with a shinui even on Shabbos proper if he has no alternative, since kavod habriyos permits one to transgress a rabbinic transgression, and doing a melacha with a shinui is a rabbinic transgression. [The same way that one can continue walking in a karmelis on Shabbos with a tallis whose tzitzis are possul, even though doing so involves a rabbinic transgression] How much more so, should he seemingly be allowed to tear with a shinui here, when Shabbos is over and it is only that the Sages/ Rabbis prohibited one from doing melacha prior to saying some form of Havdalah.
Why, then, the need to think Baruch Hamavdil? [Seemingly it should be unnecessary to do so.]
And why can’t he say Baruch Hamavdil [as opposed to merely thinking it, which is invalid according to some opinions[, as one is permitted to talk in a bathroom in a case of need, such as to stop someone from committing a transgression or for women to talk to prevent yichud – and seemingly also in this case [if one would say that tearing the paper before Havdalah involves a transgression, he would be allowed to talk to prevent this transgression – i.e., to say the words of Baruch Hamavdil, after which it is no longer a transgression to tear].