If I get a new iPhone do I get to re-download my purchased apps on original phone?

Yes, I believe so. You just need to be logged in with your original apple ID.

Purchases are tied to your account, not your device; so long as you use the same account, you should have no problem… unless you have (or have had) more than five devices synced on the same account.

Yes, and you can download them via iTunes (either on a Mac or PC) or wirelessly.

Before you upgrade, make sure you back-up your current phone to the iCloud and/or iTunes. All your app purchases will be there.

You’ll have the option to program the new one from the backup or to restore it as a new phone. If your current device is working well, using the backup sets the new one just like your old one and simplifies the process. If your current device is malfunctioning, setting it up as new takes longer, but helps weed-out any potentially corrupted files.