Yes, b/c my name is Kathryn and there are so many variations of it. I don't think it is vain naming your daughter a form of your name or exactly your name for that matter. I think she would be honored to share your name, and it is just another something for you to share in your mother-daughter connection. Don't forget that it is a tradition for men to often have forst born son named after them. If its not vain for them then why should it be vain for you. Own it! Do it! Is cute.
I don't see why not. Men have been passing on their names to their sons for years. If it's a variation of your name then I think it's different enough. You can always give her a nickname as well. The most important thing to remember: always choose a name you love.
Sure, why not? If the name was dissimilar enough so that we could avoid confusion, it's fine. I have part of my mother's name, and despite our ups and downs, I like the connection. I don't feel as though my identity has been compromised because I have part of Mom's name, and I certainly don't see her as vain. Alison and Alice are probably a bit too close, though. Maybe Alice could be a middle.