"these books were from me"? Does that even make sense in English? Shouldn't it be "these books were mine"?
"These books were mine" would be translated «Э́ти кни́ги бы́ли мои́».
«Э́ти кни́ги бы́ли от меня́» probably means I've sent them as a present or something like that.
Almost correct. This is not necessarily a gift. The meaning is just "these books were mine and I was that person who sent them".