Yes, you can combine "like" with "and so on" in that way. Your example sounds conversational. I don't think I would write it that way, except in an on-line chat, perhaps.

Yes, you may, but it doesn't sound that natural. I would suggest saying something like: "She likes reading books ABOUT history, science, and so on She likes reading books: history, science, and so on." Tell me if you're not satisfied with this answer, and we might work something out.

You can say it like that but another way is to say "She likes reading books about history, science,etc. Etc is etcetera meaning "and more" or "so on and so on".