G'day Matt,

The DIY kits have a tendency to split at the back, regardless of how careful you go...I think it's just the nature of these kinds of eyelets.
I would probably suggest heading to a local canvas & awning specialist to see if they can put one in for you & make sure it's a 100% tidy job.
These ones are a-ok for basic tarps, etc, but not sure if its something you'd want to put on your beautiful tent.

Now problem, anytime!

G'day Drewe,

Yes, absolutely, you can use the EyeletS & Tool Set on a CGear Multi Mat. 

G'day Ben,

Yes you can use these eyelets on a tent fly. Depending on the material of your tent fly you might need to add some reinforcement before adding in the eyelets.

G'day Lucy,

These Eyelet sets are really designed for use with poly tarps, or canvas, so you might find they don't hold very well on mosquito net mesh. I'd recommend cutting a small square of nylon or canvas and adhering that to the mosquito net, then popping an eyelet through that.

G'day Peng,

Yes you should be able to use these eyelets and tool set on a picnic rug as long as the rug isn't too thick.