the passing of judaism from mother to child

hope i tagged it right :/ i know that being jewish passes from a mother to her child, but i’m unsure of blurry lines?

1. if someone is adopted by a jewish woman, but the birther wasn’t jewish, is the child jewish?
2. if the situation was switched and the one who gave birth was jewish but the child was adopted by a non-jew, would they be jewish?
3. if there was a surrogate who was having a baby for a jewish family, would her judaism play into the baby’s?
4. if a trans man has a baby and is jewish, would he pass his judaism to the baby?

i’m not jewish because of general trust in goodness of whatever potential higher power there is, and a mental incapability fully becoming a faith at the moment, but i do wish to learn about this faith, and who knows, maybe when i’m ready, it’ll happen.

all that to say, i just wanna learn (even if your answer is specific to a smaller faith within judaism)