How Do I Replace The Rubber Material Around Engine Bay?
 

Does anyone know how I can replace this rubbery flap that runs along the sides and back of the engine bay?
I'm not even sure how you remove it... or if that's even possible?

Pull the old gaskets out with vice grips. Install new pieces by coating the grooves and the gasket groove parts with dawn dish detergent, then pulling the gasket along in the groove with vice grips.

For the old ones.. you can just pull it out at an angle.
There is a C-shaped groove that goes all along the engine bay that you would 'pull' the new rubber engine seal along it.
As another stated, you'll want to grease it up so it slides through.

I don't 'pull' it, I just stick the top lip in the upper groove and use a plastic spatula to push in the bottom lip.

Try isopropyl alcohol for installing rubber trim. Makes it nice and slippery for installation, and evaporates quickly so it doesn’t slip off again.

I just did this last month. I did it just as Ed suggests in post 4. Easy with a plastic pushing tool. Mine was a plastic doortrim tool that comes in a kit of 4 or 5 pieces designed to pop door panel clips and similar.