The card will fit but that all depends on your case.
Do you have much room or have any other cards in the other slots?
I wouldnt suggest going with a 550ti , they are'nt that great, you rae better off getting a 560 or a 6850/6870.
Also yes you will definately have to purchase a better psu for one of these cards.
No i only have a gt 440 no others and these are rough measurements:
7 inches wide by 15.9 inches high by 16.5 inches deep and the 550 is 2x bigger so i dont see how it would fit..