Chevy Cavalier (2002) - Cracked Dashboard and Stereo Installation Questions

I have a few questions about a Base Model, Two-Door Coupe, 2002 Chevy Cavalier that I just recently got. Some patience, and helpful replies, would be greatly appreciated.

As seems to be the case with most/all Chevy Cavaliers, the dashboard is badly cracked. This one is majorly cracked in at least a couple places, which causes several issues. Besides being ugly/bothersome to look at, it causes a squeaking noise when driving at high speeds/hitting bumps in the road, which is super annoying; it also seems to be letting in outside air, which sometimes causes the inside of the windshield to be fogged up, which is also really annoying.

I am thinking about trying to get a dashmat/dashboard cover online (eBay, Amazon or Walmart), which I should be able to get for around $30 shipped, and that will help with the ugly appearance of the dashboard; but I'd also like to try to stop the air from leaking up to the windshield and fogging it up, and also stop the squeaking noises from the cracks.

As for the cracks in the dashboard, I was thinking about trying to use Gorilla Glue to glue the cracked pieces back together, which should stop it from squeaking so much; and I was thinking that it will likely also help to (at least) minimize how much air comes up to the inside of the windshield. Has anyone else tried using Gorilla Glue (or something similar) to fix cracks in one of these dashboards? If not, should it likely work?

My other question is in regards to installing an aftermarket stereo in a 2002 Cavalier. From what I've gathered online, it looks like it's pretty much going to be required to take off the entire dashboard (which will likely take at least an hour or more); but I'm not sure about this. So, to anyone who has installed an aftermarket stereo in one of these Cavaliers, is there a way to remove the factory stereo and install a new one without taking apart the entire dash? Or is this the only option?

I was honestly thinking about trying to just cut out parts of the plastic dash covering the outer part of the stereo area, to get access to the screws holding the radio bracket in, and then attempting to glue the pieces of plastic back together after installing the new stereo. I was thinking that a Dremel tool might be able to easily cut through the plastic and not damage much of it. Anyone think this might be a good idea? Or would it likely turn out badly? And is taking apart the entire dashboard just to install a new stereo the only option?

Sorry for the lengthy post. If someone actually reads this and would offer me a helpful reply, I would definitely appreciate it!