Rat damage? Not likely, rats are not so suttle. I think the rats will be an issue when your tortoises are cold/torpid, and gnawing rats may do extensive damage or even "steal" hatchlings.
The crack in the beak I would guess it just one of those things, or possibly two or more tortoises were competing for the same food item, and one grabbed her jaw. They can bite pretty hard, as evidenced by ornery males damaging females or nipping at your toes if you don't pay attention and they are hungry... Yes, you are right, the beak grows and is not real sensitive, similar to your nails. A bad fracture or chip might require trimming, which a vet will do or you can do yourself if you are confident (first time I did it was real scary, but it turned out fine, using a Dreml type motor tool on a rehab/rescue tortoise). I think the damage on your tortoise is minor, and it will probably heal up fine on its own, keep an eye on it for complications and smooth healing. I assume you provide cuttle bone and Calcium sources, many of which may keep beaks in trim.
Wage war on the rats. I will wonder why you used a hose rather than a machete on them...but I have grown cold in my old age and perhaps you are more gentle. Fencing them out is the best, as they will come back and you can never kill all of them.
Good luck,Vic