If I start wearing my retainer again, will it straighten back out my teeth?

Depends. If it is a very small movement then perhaps, otherwise no.
Possible. May want to consult your orthodontist to see magnitude of tooth movement.
Oh, my. All that time, effort, and money lost. If retainers not worn teeth will shift. If they shift, putting retainer back in may recover some of what has been lost, but result has been compromised and is now less stable. Please get back to your orthodontist to check the way the retainer fits...You don't want it to do more harm than good.
Possibly. If they have not moved too much and you can still get the retainer on, then yes, it will work much like invisalign and will move your teeth. But the move they have shifted the harder it will be to wear the retainer initially.
Make sure it fits. Make sure your retainer fits ideally. If you haven't been wearing it, you're teeth would have definitely shifted. You may want to check with your dentist on the fit, and if you need new ones, they can always be made to your current position. Sometimes, you may need more ortho treatment as well.
Maybe. Depends on how much your teeth have moved. If just a little, then your retainer will correct minor issues fairly well, but only if worn full time for several weeks. If more then you may need a retreat and new retainers.
Maybe. How long has it been? Did you finish your braces as a teen and now you're 33? Then it won't work. Retainers are passive devices aimed at keeping your teeth where they were put, not active devices. But you might get lucky! If it almost fits, give it a try.
Yes, but. If it has been too long, your retainer may no longer fit. Don't force your teeth into a retainer that doesnt fit-- see your orthodontist for advice.