One may not carry a Megillah to shul on Shabbos Erev Purim (this year 27 Feb) even in a place with a proper Eruv because one may not prepare for Chol (i.e. Purim) on Shabbos. Rather, one should bring the Megillah to shul before Shabbos, or after Shabbos. Shaarei Tshuva 693:2, Kitzur Shulchan Aruch 141:7
On Taanis Esther one is permitted to bathe, listen to music, and to wear new clothing. Taanis Esther is different than the other fast days because it is unrelated to the destruction of the Bais Hamikdash. S’U Siach Yitzchok 360, Piskei Tshuvos 686:2:6
The Kav Hayashar says that one who needs mercy from heaven regarding any matter should take time on Taanis Esther to say chapter 22 of Tehillim and then pour forth one’s request to Hashem and mention the zchus of Mordechai and Esther; that in their merit Hashem should respond, and open the gates of mercy, and accept the tefillah willingly. Kav Hayashar 97, Yesod Veshoresh Ho’avodah Sha’ar Hamifkad pg. 263
{halachafortoday.com/Matzav.com Newscenter}
I think another point could be added to rabbi brazils vurt and that is the importance of ki tov lo imuch which is the first one of the mishpatim and so if we are ki tov lo emuch one jew to another judging others favorably e.t.c. (in this case a slave but it can be applied to the general population too I think) then hashem will be ki tov lo imuch with us too and give us the protection of the mezuza which is symbolized here with the gimatriya, and I guess from this is derived the importance hashem places on our treatment of other human beings by placing this commandment as the first one pertaining to the laws