I'm reminded of my father in laws practices. Measure twice, cut three times and then just shove it in place.

They make epoxy coatings for just such a use. Some businesses do only this for customers.

Lots of concrete doesn't have a coating however. Think about driveways, sidewalks, parking lots, street etc.

If you want your floor to be perfect then a coating is the way to go. Otherwise, it's probably fine.

A crack is a sign the foundation is sinking. Some cracks formed when the house was built and settled and are fine.

Others are not fine.

Maybe I'm not the most experienced with this but why does it matter if rats get in there? How are they ruining it?

I'd put some d-con all over it and not worry.