All of the questions are designed to help you observe exactly what is happening on the bike when it is working correctly (forward motion) and when it is not (backwards motion). It may take many repeats of tests to see everything that is happenign, or it may be obvious where the problem is pretty quickly, but careful observation will show you where the problem is.
Without actually being there to see and feel what you have and how it moves and stops, I can't tell you what might actually be happening, but there are a limited number of possibilities.
It's the rear wheel that's not rolling. It's the same case when upside down and when I manually rotate. I can rotate the rear wheel with some applied force but it stops abruptly meaning it's not possible to let the wheel spin freely.
Well, since the rear wheel spins forward freely but not backwards, does it stop instantly when you rotate it backwards after rotating forwards, every time?
Or does it take some distance to do so?
If so, how much rotation does it make?
Does the cassette's freehub click during this like it does in forward rotation?
Or is it silent until it stops the wheel from rotating?
I'm not sure what you mean by what other part of the bike also moves while reverse rotating. I don't think any other part if I understand what you're asking.
If the chain is touching the cassette then the chain should move too. If it doesn't, then the chain is jammed and you should find out what's wrong with the chain or replace it. If it isn't the chain itself it would have to be something the chain is attached to or passing thru.
If the chain is not touching the wheel or the cassette, then it won't move with the wheel.
If the chain is touching the wheel or cassette, and also touches some other part of the bike, does that other part also move when the wheel stops? Like the derailer? Or the chainguard or front derailer, if any?
If the chain does touch wheel/etc and stops moving when the wheel does, does it have more tension on it then?
Does pulling on the chain from the "top" (like the front chainrings would) also spin the wheel forward?
Etc. Observing what moves and what doesnt' move and what causes other parts to move will find the part stopping it from moving.
I'm not able to get the chain off the cassette right now since it's indoors and handling the chain is pretty messy. Maybe I'll take it into a bike co-op tomorrow that's supposed to be open. I appreciate your help in trying to help me troubleshoot this.
Since you don't have any cranks / motor / etc on htere, which means you have no front chainring, then if you have gloves, or some paper towels or a rag, etc, it's pretty easy to shift the derailer out all the way to the right, then sipmly lift the chain off the cassette's teeth, and either ziptie or hold the chain away from the cassette so nothing can possibly restrict wheel movement except for the wheel itself.
Then it is easier to tell if
A) the wheel is catching on something on the frame, or a brake arm / pad / etc that it doesn't do in forward motion
B) the cassette is jamming on the frame and it's built in freewheel allows forward motion anyway, while preventing reverse rotation
C) the wheel now rotates freely meaning the problem is with something the chain itself passes thru, like the derailer and it's jockey wheels, or the front chain guide/derailer if the bike has one.
Etc.