you very well could do it with one card. almost all of the newer cards have dual vga or dual dvi outputs on them. to go with your first idea, you could get a dvi-to-hdmi cable for one output and a dvi-to-vga(which comes with the card generally) and vga cable to go to the other. this leaves room if you have an hdmi capable dvd or such to put in the other hdmi slot.
your second question i'm not sure of. your going to need pretty good card to support the hd really well. i'm sure someone else on here can help with better info than i can guess at.
for your third question. dvi is the better vid quality. thats why i'd do it like i first said and use the vga input for your browsing. hopefully this helps and i didn't just ramble on since its late. good luck