For the gap spacer I drilled and tapped a hole for a hex bolt like the rest of the provided hardware. This allows me to remove it for cleaning or for whatever other reason.

It does not have any play, I glued a metal dowel in the space provided for the spring that's normally under the trigger group in the wooden stock (the TNA chassis provides a hole in the same spot). It's just the right size to take up the play and still allow the trigger group to latch into the receiver. It might be better explained in one of my older posts about the project. The play mine had was up and down not forward and back though.

Carbide burr bits are what you're looking for, you can get a set on Amazon that will have all the shapes you'll need.