you have to put the 6 pin pice connector otherwise most likely the card will not let the system boot.....a 450watt psu will power that card perfectly fine...if you do not have a 6 pin pcie cable to attach to the card you could get a molex to 6 pin pcie adapter and hook the card up that way
that depends on the psu models, your full specs etc. as the psu will supply power to all components in your pc, especially to your cpu, motherboard and gfx card.
instead of beating around the bush, state the psu models you're comparing. the 7770 will be able to run on a typical 500w psu which includes generic psus. if the 450w psu is low end, a psu upgrade might be in order.
for example, a corsair cx 430 v2 can run a 7770 more reliably than a zebronics/iball/intex 500w psu.