I need to factory reset my phone.
However, I need to know whether I will be able to download
the applications I paid for on Google Play once I do the
reset, and download them onto my phone at no additional cost.
If once I do a factory reset I need to pay again to download
all the apps, then is there a way to back them up prior to
doing a reset, and then reinstall them back again?
Even if you don't back up downloaded applications you can still download them again, your play store will show you the list of all installed and downloaded applications even after factory reset you can download any paid or free application again. Once you have paid you don't need to pay again, you just log in by your google account and you can download all them again. But backing up applications is a better way, it will automatically install all your applications.