I don't understand when to use jsi and when to use jsi ty.
Jsi and Ty jsi are the same. The subject "Ty" is often omited because the meaning is obvious without it.
Same problem. Can I always write "Jsi" without "Ty"? Are there any exceptions?
Yes, there are. You will meet some in the course. Where you are directly referring to YOU, ypu will need it.
Okay. Thank you
Why "you are frantisek" is 'ty jsi frantisek' and "you are a child" is just 'jsi dite'?
What makes ty disapear?
Ty and similar personal pronouns are optional and used for stress. See the Tips and notes.
Why "Jsi ty dítě" is wrong?
When you stress "ty" by adding it here, it should go to the first position. And "jsi" to the second unstressed position. "Jsi" is sometimes clitic, so it is "at home" in the second position.