1) I have a question about personal pronouns and possessive pronouns for genitive, dative, and accusative declensions. My textbook lists two versions for each gender in those cases. My question is, which version do you use when? Does it matter? 2) Also, for the possessive pronouns muj and svuj, is there any rule for when you use which when it is not a question of who owns what? For example, I understand if you were differentiating between "Mam svoje tuzku a toje." But when you are talking about your objects alone, is there a rule? Does it matter if you say "To je svoje kocka" or "To je moje kocka"? Dekuju moc!
Ad 1) I guess you mean já - gen. mě, mne; dat. mně, mi; accus. mě, mne, etc. Usually, the first version is commonly used. The second one is considered as standard and it also helps to decide about the right spelling of the version with -ě-, as the pronunciation is the same. Ad 2) Possesive pronoun svůj, svá, své is always related to the subject of the sentence. E.g. "Mám svou tužku a tvou tužku." or "Vylil svou kávu na mé kalhoty" x "Vylil mou kávu na své kalhoty". If the subject is not overtly expressed, or if it is just a formal one (like in constructions "to je, to jsou"), svůj-svá-své pronoun cannot be used. "To je moje kočka" is the only possibility here.
If I may add something... What decides about the form of the personal pronoun is whether it is preceded by a preposition or not. Without a preposition: Prosím tě. After a preposition: čekám na tebe. The case can be also whether the pronoun is at the beginning of the sentence or not. If this is true, then the longer form is more often used. I hope it's correct.