1)
返してもらおうか? is a word being said to HER, i.e., a request/order to her, weareas 返してもらうか? is said to HIMSELF. "
He isn't saying that sentence to anyone, just thinking it." shows that that's the latter and there's no typo. (In this case, he is saying to himself what he is going to do from now on.)
3)
Two interpretations are both possible; 1)the speaker doesn't know the giant girl is an actress now and 2)the speaker doesn't think actress is a huge success in life(大出世). In either way, 大出世 is contrary to fact for the speaker. The context must show which is correct.
As for 話のタネ, the speaker thinks that a fact that her sister becomes giant could be a thing to talk about if her sister got success in life, i.e., she can talk about her sisiter to other people, but actually she feels that her sister is just a shame to her because (she thinks) her sister didn't get success in life.
4)
「私が何をしたからこんな目に遭う」って言うの? makes sense? The speaker is asking WHAT the cause/reason of her trouble is, not "she got trouble because she did something(= 何か)". (Probably she thinks she did nothing wrong, though.) The meaning is close, but the nuance is different, just like そこで何をしてるの vs そこで何かしてるの.
Also, I found this sentence 私に何の関係があるというのだ. Here, the subject of という is "I", right?
No. The subject of いう is "you" or "people in general", as lanthas-san pointed out.