Hi there, good to have you here at TC. I moved your thread because although it is an introduction, you are also asking lots of questions and I thought you'd get more answers if the thread was in here instead of introductions.
So sorry to hear that your little one has been picked on and has ended up with no claws. I'm sure he will adapt just fine to sitting on perches etc, they are very good at just getting on with things. I've never had to hand feed a cockatiel so I don't know how or how often you do it, somebody else will be along to put you right on that. I don't think you can house a cockatiel with budgies, budgies are bullies and they don't always get on with cockatiels, so although they can have supervised playtime together, living together just might not work.