Almost by definition he'd have to "speak" Hebrew enough to quote the scriptures as much as he did, but, to use an example relevant here, it'd be like saying that Francis speaks Latin while his birth language and primary language is Spanish.
Hebrew uses the same writing system as Aramaic, and there's some shared vocabulary and some grammar structure similarities (putting a v' sound before a word means "and," plurals end in -in similar to the Hebrew -im, etc.).
I have a hard time believing that Jesus didn't know Hebrew, but yes, he probably spoke Aramaic in his daily life and travels.
Yep; as he was able to read a Talmud or Torah scroll, I would say both.
The Talmud was written centuries after Jesus.
