1- They are very social if you teach them to trust you. They'll love you and puke on you so much you'll get sick of it.
Towards other birds, they can be social (I've had one budgie try to seduce my female kakariki) but it's risky. Remember they're small birds. If the other bird is bigger, your budgie will not stand a chance in a good fight. Even if it tries to win.
2- Extremely smart. They are afterall little parrots. And it shows that the brain size doesn't matter much.
YouTube - snoogly's Channel See this youtube user's video, he has a budgie named Sven that I just LOVE. They'll talk and play and learn tricks really well.
3- They can bond with you as well as any other parrot. Size doesn't matter.
Mind you in budgies I find it easier to have males. Females will usually not talk (I've seen it but they're usually not interested.), they can be extremely bossy, territorial and bitey. But frankly? My favorite budgie was my female, the one I had first. Just because I loved her independant nature. I was her chewtoy and I lived up to the cause.
Always buy just one budgie first EXACTLY because of how social they are with other budgies. Otherwise you'll have a hard time teaching them to trust you. After you got one tamed to the point you want (after a year I'd say), get another budgie and normally the first one should teach trust to the second one. Like "Come on, the human's fine to play with!"