1) Is one allowed to listen to Jewish music in the bathroom? The words may be from tanach or Gemara.
2) the Halacha is that if one puts on 2 garments at the same time he can forget his learning. Does that apply to two outer coats that are not connected to each other?
3 if one finishes shema after the chazan says the last three words but started with the tzibbur so he didn’t say kel melech neeman what should he do?
4) is one allowed to say birches hashachar while walking to the beis medrash if it means he can immediately start learning upon reaching the beis medrash?
5) is one allowed to learn during chazaras hashatz?
1 No, this would violate the prohibition of thinking Torah thoughts while in the bathroom.
2 Yes, this would seem to be included.
3 In order to fulfill the 248 words of Shema, one should listen to the ש”ץ repeat ה’ אלקיכם אמת and have in mind with that to complete 248. If one misses this [he is still in middle of Shema], the Magen Avraham in Siman 61 brings another option to have in mind the 3 letters of אמת, and this fills the 248 as well.
4 Strictly speaking it is permissible to say birchos hashachar while walking. However being that this generally greatly detracts from a person’s ability to properly focus on the meaning of the brachos and say them with intent, it would seem not worth the extra few minutes he gains by doing so. If one is late for a shiur or chavrusa perhaps this would be justified.
5 It is prohibited to learn verbally during Chazaras Hashatz. To learn non verbally [thinking] would depend. If one can also concentrate on the bracha being said so that he can say amen and know what he is saying amen to, this would be permissible. Many are stringent not to learn at all, so as to give their full concentration to the brachos.