1) The final meal before Tisha B’Av is called the seuda hamafsekes and has special requirements. The purpose of the seuda hamafsekes is to experience sorrow and mourning for the destruction of the Beis Hamikdosh. (M.B. 552:1) Therefore, it is prohibited to eat meat or drink wine at this meal. (Although the custom is not to eat meat or drink wine during the Nine Days, during this meal it is prohibited and not merely a custom.) In addition, one may eat only one type of cooked food, so that the meal should not be one of honor and pleasure. (S.A. 551:1 M.B. 11, 17) The custom is for the seuda hamafsekes to consist only of bread, cold hard-boiled eggs and water (Rama 552:5, M.B. 13).
When Tisha B’Av occurs on Shabbos and is postponed until Sunday (as it does this year), the seuda hamafsekes (Shalosh Seudos) does not have the restrictions cited above. One may eat meat and drink wine and his meal may consist of many cooked dishes. (S.A. 552:10) Unlike other Shabbasim, however, he must stop eating before sunset.
2) Learning Torah on Tisha B’Av is prohibited, except for those portions and topics which are relevant to Tisha B’Av and mourning. (S.A. 554:1)
There is a debate amongst the poskim whether one may learn Torah on Shabbos when Tisha B’Av occurs on Shabbos (and is postponed until Sunday). Many poskim maintain that on Shabbos after noon, one may only learn these portions and topics of Torah which are permitted on Tisha B’Av. (See Rama 553:2 and Netai Gavriel page 522) According to these poskim Pirkei Avos is not said. (M.B. 9) Other poskim hold that since eating meat and drinking wine is permissible, learning Torah is also permissible. The Taz concludes that one who conducts himself according to this lenient view (even after noon) is not acting in error. (M.B. 10)
3) When Tisha B’Av occurs on Shabbos and the fast is postponed until Motzei Shabbos, one may not prepare for Tisha B’Av on Shabbos. Therefore, one may not bring copies of Eicha, Kinos or stools to Shul on Shabbos. (Netai Gavriel page 533)
4) When Tisha B’Av occurs on Shabbos, the customary Havdallah is not said on Motzei Shabbos. Rather, on Motzei Shabbos after nightfall, the bracha of borei meorei haeish is said upon seeing candlelight. The bracha should be recited after Maariv before reading Eicha. However, if he forgot to say it before Eicha, he may say it any time during the night. The bracha over besamim is not recited. (See Halachos of the Three Weeks by Rav Shimon Eider page 17)
5) The Gemara tells us that the Beis Hamikdash continued burning until sunset of the tenth of Av. Therefore, the restrictions of the Three Weeks and the Nine Days apply until noon of the tenth of Av. (M.B. 558:5) Therefore, one should not eat meat or drink wine until the noon after Tisha B’Av. Bathing, haircuts, washing clothes and music is also prohibit. (M.B. 2) [Regarding Havdallah, some permit drinking wine while others advise to use beer or chamar medina- for normative halacha, a rav should be consulted.]
Rav Shimon Eider zt”l (Halachos of the Three Weeks page 32) writes the following, “When Tisha B’Av falls on Shabbos and is postponed until Sunday [as is the case this year], eating meat and drinking wine is permissible Monday morning. On Sunday evening, however, it is prohibited … since the day was spent in mourning, it is not proper to assume conduct of simcha (i.e. eating meat and drinking wine) immediately after it is over. Bathing, washing clothing and haircuts are permissible Sunday evening. Music is not permitted until the morning.” Harav Gavriel Zinner shlit”a, however, permits music on Sunday evening as well. (Netai Gavriel page 553)