Using an iPhone bought app on a new iPad 2, or do I have to purchase them again?

So I'm selling my iPhone and getting an iPad and I have previously bought GarageBand and Xewton Music Studio (which was rather expensive for an app) for my iPhone. Now if I buy an iPad 2 will I be able to run these apps on the iPad 2 or will I have to re buy them again?

You should be able to download them on your ipad for free because you have previously bought them

As long as you have an apple account, you should be able to transfer them over.

Sign into your apple account, go to the app store on the device you want to use it should just download.

Yes you could run them fine, though if the app is not optimized for the iPad's display you could run them in 2x mode.