I used to have a rat problem with them hanging out in my engine bay and it was resolved after boarding up some gaps but looks like they're back at it. There was a clump missing in the left pic that was taken earlier this year and you see an obvious hole in the right pic.

I sprayed peppermint oil into the insulation for it to soak but for now...
1) that big of a piece wouldn't have been able to fall off from regular driving conditions, right?
2) Is the insulation something I need to worry about? where it would effect the car?
3) might be a dumb question but if I were to fix it, would I be able to DIY and re-stuff that section? of course I'd buy the right type of insulation. Not sure if it's actually a full piece that's secured to the body?
4) what's it actually called? can't find anything that shows that specifically

 

Go out and buy about 5 Victor rat traps and place them appropriately near the car. Load them with Fluff liquid marshmallow - works every time - then get rid of the bodies the next day... I used them for mice in my garage last winter and got every one... For me, I wouldn't worry too much about the missing insulation but I would take action on the rodents. GOOD LUCK!

 

Firewall insulation is installed before anything else goes into the engine bay.