I've realized after going through my books that I tended to buy them from all sorts of places. This includes a used book store where the person stamped inside the book, on the title page not the cover and marked with marker at the very bottom of the book. Should I just donate these or are they allowed to posted here?

I also own manga, is that allowed here? Some of these also have the marker at the bottom of the book.

Manga is absolutly allowed to be posted, as long as it's in the traditional book format (not stapled like a comic book) and has an ISBN.  :)

Markings from retailers and booksellers are allowed as long as it's not obscuring any text, and the requestor does not have an RC against it.

 I would not post it, the help document says:

 BookCrossing books may have stickers or stamps or markings on the outside or inside covers or page edges of the book; this is OKAY. These may not obscure text.

 So while the reminder marks on the page edge is postable, it does not say the title page is ok, just the inside or outside covers and that they may not obscure text.

 (I could be wrong, as always)

As long as the stamps & stickers don't obscure text, they're not specifically ruled out. 

The postability criteria help doc says:

If you feel your book falls into a "grey area", you can either post the book and send a Personal Message to the requestor, or not post the book.  We have delineated what we can, and we expect members to follow these guidelines, and use their common sense in cases that are unclear.  If you would not mind "paying" a credit for a book you are considering posting, then it is probably okay to post.  However, book condition can be a subjective matter.  Keep in mind that a pattern of sending out poor-condition or inappropriate books will jeopardize a sender's membership.

Since an author's signature is okay on the title page, I would tend to think of a sticker/stamp on the title page as the same thing.  It doesn't obscure any text either.  Having said that, I also agree with Joy.  Would you mind receiving a book in this condition?

The ex-library book section of posting criteria says "Ex-library books often have stamps inside or on the binding or on the page edges: this is fine." and I can't see a bookstore stamp being any different than a library stamp so they should be just fine to post. I wouldn't hesitate to post one with a stamp or writing on that page that doesn't obscure text.