It's not a huge deal. I'd never rely on a proprietary backup format, but rather copy files somewhere else (it could be an external sd card or a pc) on an individual basis. If you want to retain app settings or game states, you can copy the whole .android filder and simply put it back later. Check for any apps that store data in their own folders that are subfolders of the root folder, too. Contacts should normally be sync'd with Google, so would come back when you sign back into your account. You can also export from within the Contacts app as a belt-and-braces (back that file up too). If you want to keep text messages, and app like SMSbackup can do that for you, and I think there are also apps that will take care of call logs. If you have an external sd card, it's a good idea to remove that before re-setting, just in cse the process wipes that too.
You won't have to re-install Lollipop: the phone will revert to an out-of-the box state, but with the latest OS in place. When you sign back into your Google account, choose the "restore" option and things like wallpapers and your apps will be put back. You'll need to set your homescreens up again, so screenshots or paper notes are a good plan. If you have to do the process manually, going into Play and choosing My Apps, then the All tab will give you a list, so at least you don't have to go searching.
If you do a reset, you should find the problems you've encountered so far, as well as others should go away. What the process does is to get rid of any bits of code left over from the old OS that are hanging round and confusing the system.
That all sounds complicated, but I've tried to cover all the bases.
