peakpilgrim, Hi.
Rats are really clever, and can spot a trap a mile away.
As for getting in via a flat roof, never seen that, as previous posts they tend to use existing access holes as ducts into the property, if you cover even the air bricks with a firmly fixed wire mesh this "should" keep them out as well as [if the mesh size is small enough] deter [especially in late Autumn] Field mice who at that time of year in a Rural location go looking for "Winter - warm - accommodation"
As for what rats can and will eat? you name it ! I have seen an Electrical Cooker cable have its outer sheath totally stripped over a length in excess of 2 Meters. then the little brown furry beasties stripped the insulation from the cables themselves, but did not get harmed? [no corpses] what they did was to remove the insulation from the actual wires themselves, BUT on opposite sides of the cabling, leaving two layers of the insulation between each conducting wire, when the cooker was switched on ! BANG. the circuit tripped.
As a foreman on a 100 + year old brewery in Edinburgh I recall that all of the exposed ceiling ties were "rounded" on their top surfaces caused by the action of the rat population using the ties as a "rat run" over an area of floor. this is the only place that I have seen truly Feral Cats that were capable of taking on some of these lather large rodents, if anything the cats were worse than the rats?
Enough of this.
How about you place some external "rat bate traps" in secluded dry locations around the house? in effect creating a perimeter "barrier" to the rats [and field mice] once installed a quick look at them will tell you if they have been accessed by the rats.
As for using an Air Weapon? having had a recent rat "attack" myself an old building [derelict] was recently demolished so our furry friends "migrated" I saw a couple of them in my back yard, but, although I have a very accurate Air rifle, and regularly take part in air rifle competition's, because of Scottish Air rifle legislation I was not able to dispatch these furry pests, I had to subject them to poisoning, it worked but was not a pleasant end, even for a rat.