Quick question, I know that Můj is masculine and Moje is feminine/neutral, but how do I know when to use those instead of mě/mí/mou? Or the other way around as well.
Same question when using Tvoje/Tvůj or Tví/Tvá/Tve?
These are differnt grammatical cases. Review the Tips and notes or some other resource, like e.g., https://en.wiktionary.org/wiki/m%C5%AFj#Declension
No it is not, the table you inconviniently cut out without context is all just about the feminine pronoun her = její, the masculine pronoun his = jeho is in a different table. The genders in the table refer to the gender of the owned object.
Nemělo by být v otázce pomocné sloveso DO? "Who does have her bear?"
The English translation shows on the page as 'Who's her bear', which is surely wrong?
Why is it "jejiho medvěda" (ho + a) and not just simply "jeji medvěd"? What would be the difference?
Jejího medvěda is in the accusative case, as the direct object of the verb. Její medvěd is the nominative case form, which would be used for the subject of the verb... which it is not in this sentence.
Maybe this sentence should be deleted, because it is confusing when the Accusativ is not taught yet.
Information about the accusative case can be found in the Tips and Notes for the Food and Animals Skills at https://www.duolingo.com/skill/cs/Food/tips-and-notes AND at https://www.duolingo.com/skill/cs/Animals/tips-and-notes. (This exercise is part of the Animals Skill.)