I was wondering about books that are otherwise in good condition that have an "ownership" sticker inside the front. For instance, "This book belongs to _____"

 or, for instance, someone wrote a note to you inside the front cover. (I know that sounds awful to give it away, but I don't have room to save books forever!)

Are those postable?

Yes, an inscription or nameplate inside the cover is okay to post.  It's writing on text pages that makes a book unpostable, not on endsheets or blank pages.

That's OK. As long as it doesn't affect the text at all or have a bunch of stickers all over the book.   Half the books on PBS would be unpostable if they disallowed those things.  Most book stores, especially UBS put a sticker or stamp or something on their books. You can PM the person who requests the book before you send it out just to be sure. But if you do, make sure to give them a deadline to respond before you go ahead and mail the book.   But you don't have to pm them first.  Those things are allowed.  Now if your name is written on every page or there's used book store stamps on the text-that wouldn't be good.