I have been learning Hungarian since I wereas a baby.

I have been learninged this language at home in Hungary at home.

I have beenstarted learning German sincwhen I was eight years old.

Your version implies you are still learning German. Presumably, you are fluent at this point (since you have it listed as a native language), so you should not use the continuing past tense "have been learning".

I have been learninged German at home and in my schoole.

Same problem as above.

I've been liveing in Austria since I amwas eight.

Here the continuing tense is appropriate :)

I have been learning Hungarian since I wereas a baby.

I have been learning this language at home in Hungary at home.

I lived in Hungarythere for seven years and I still go back there.

I also speak German.

I have been learning Germanit at home and in myat schoole.

I have lived in Austria since I amwas eight.

I have been learning Hungarian since I wereas a baby.

I have been learning this language in Hungary at home.

This sentence is grammatically correct but since Hungarian is your first language and I assume you speak it fluently, I would instead write:

I learned this language in Hungary at home.

If you're still learning and not fluent yet, this sentence is fine but makes it sound like you live in Hungary still, so I would recommend "I have been learning this language in Hungary and at home." This conveys that you practice Hungarian every time you go back to Hungary as well as in your house with family in Germany.

I have been learning German since I was eight years old.

I have been learning German at home and in my schoole.

I have lived in Austria since I amwas eight.