Will I ever lose the apps that I've bought? Say I've bought an app for $0.99. If I delete it, and then I require that app again, do I need to pay another $0.99?

(OK, I really don't want to waste $0.99 just to try it…)
You'll have all of your apps for the life of your iTunes account, and you can download them again at any time for no charge.  

The only exception is apps that have been removed from the App Store for legal reasons -- generally copyright violation of some form -- or if they're removed by Apple due to some rules violation, both of which are very rare.

Apple has been gradually improving its App Store interfaces so it's easier to determine which apps you already own. Until recently if you saw an app in the store that you already purchased the link to access it would still have the price: if you clicked it and you already owned it you'd be presented with a dialog that indicated that you'd already purchased it and asked if you just wanted to download it again.

As of now the App Store app on the iPad now intelligently replaces the price with "installed" if you have it installed (and, I believe, "install" if you've purchased it but it's not on the device), and the very latest iPhone App Store app seems to be doing it now, too. iTunes 10.3 appears to be doing it as well.