1) "Jedu do Česka." and "Jedu na Slovensko" are the only correct versions. We also say "v Česku a na Slovensku". There is no logical explanation for this other than we use the prepositions based on historical conventions, how they were used in the past. You can find some similarities to help you choose the correct preposition, but they never work 100%, so it's better to learn it by heart. 2) "Pomoci" is used in written language, is formal and in spoken language slightly old-fashioned. Until recently it was the only accepted form of the verb. Nowadays, also the newer form "pomoct" is correct and it's preferred in spoken language. 3) The difference is in the verbal aspect. "Hrát" is an imperfective and "zahrát" is a perfective verb. 6) "Opakovat" is imperfective, "zopakovat" is perfective. 8 "Pít" and "jíst" are imperfective, "napít se" and "najíst se" are perfective (and reflexive) 4) It's not totally necessary to use "si" in this sentence, but "smět" is one of the verbs that can be reflexive and it sounds a bit more polite if you use it. You also emphasise the fact that it's you putting the books on the table. 5) It's grammatically correct to use "si" twice as both nesmět and vzít are reflexive, but it sounds a bit odd and we mostly prefer to use only one reflexive pronoun in such cases. 7) Mohl bys mi pomoct se to naučit. or Mohl bys mi pomoct a naučit mě to? 9) Imperfective verbs have all 3 forms (past, present and future; eg. pil jsem, piju, budu pít in nom. sg.), while perfective verbs have only 2 forms (past and present; in this aspect, however, the present is indicating future, because the verb itself is used for one-time, finished actions). Then "jím" (imperf.) means "I eat right now", "budu jíst" (imperf.) means "I will eat in the future", and "najím se" (perfective) means that you'll eat and finish the eating. If it makes sense. The sentence "Alex si je vezme a čte si je." is ok. "Čte" is imperf. so there's no indication if he finishes reading it.

1. Jedu do Česka. BUT - Jedu na Slovensko. 2. Rozdíl není žádný - je to totéž slovo. (it is not the difference). 3. zahrát - budoucí čas (future form), hrát přítomný čas (present form - now). 5. Chyba ve větě. Mistake in sentence. Correctly: Nesmí si vzít (něco). Only once si. 6. Opakovat stále dokola, např. slovíčka. Repeat all the time, for example vocabulary. Zopakovat = říct to znovu jen 1x. Např. na konec přednášky zopakovat (shrnout, znovu říct) nejdůležitější myšlenky. Zopakovat = repeat only once. 8. is the same as 3. Napít, najíst (budoucí čas) future form; jíst, pít přítomný čas - pressent form - now.

Mohl bys mi pomoct mě to naučit se to? - I cannot place the "mě to", why is it there? I would say Mohl bys mi pomoct se to naučit? (Can you help me learn it?) OR Mohl bys mě to naučit? (Can you teach me that?) In the sentence you made there is a pronoun ME (mě, mi) and it (to,to) two times, which is a bit too much.