1) Can you enchant a Spellbook?
Yes, as an example look at Boccob's Blessed Book in the DMG.
2) a) How could you create a Spellbook that could not be damamge or would repair it's own dmamage?

b) How much would this cost?
Can't answer that one off the top of my head. Would require a lot of digging around.
3) Out of simply curiosity, can a Spellbook be intelligent and/or act as one's familiar?
Yes. Since there are magical books, such as the one listed above, they could be made intelligent. Note though, that this cannot be applied to all spellbooks. The rules state that items containing charges (wands, scrolls, and so on) cannot be made into intelligent items. The rules treat spellbooks as collections of scrolls, so a normal spellbook wouldn't be eligible.
Making it into a familiar is another story. I can't find any specific rules about making an intelligent item into a familiar, but you could use the rules presented in Pathfinder about making an item into a familiar.