Nope, you don't get that kind of button which is a little confusing. It can look like you're buying stuff again, but once you click buy, it will say "you've already coughed up for this, so you can now have it for free" or words to that effect. Not quite the same thing of course and not nearly as easy... but c'est la vie.
Been playing Civ just now - quite good, especially for nowt.
You'll need iTunes to buy without the phone. I know you hate it but it's great for backing up your phone when you do a sync - helped me out on more than one occasion. You can redownload apps for free if you delete them off your phone so it's not a huge deal if you don't want to use it - having all your other data backed up is mighty useful though. Are you going to use one of the Windows management apps?
Might be worth buying now anyway as it's 25% off for an undefined period. I haven't got it as I'm generally really good at buying these sorts of things and then doing precisely nothing with them. Can't say I'm not tempted though...