I'd honestly go 16" apart(I'm assuming this is for running the furring vertically? Minimum 8 feet?). 5/8 drywall isn't light and humidity can affect the wood and cause it to warp, leaving you with more problems.

The better it's fastened the better your finished product is gonna be. It seems like a lot but do it right now so you don't have to do it again later.

As for tapcon size, 3/16 is fine. For length id go with a 2 1/4" tapcon(also depends on your location as a 2" will do but for my region they don't have them). Also, get a flat head Philips or star drive, no hex heads as the hex heads will either stick out or youll have to drive them so deep that you can split the wood

For the furring strips for the drywall, any wood screw should do. Some people use drywall screws but as a drywaller, they're not meant fasten wood together like a wood screw, they're also brittle compared to a wood screw.

As for your spacing for the concrete furrs, are you using that to hang drywall as well?

That's why you use locking pliers and the rod you use to wind the spring to hold it in place when tightening anything.

And when winding the spring, keep your body to one side(the non spring side) to avoid injury.

But you are right about the spring exploding, it's happened before(not to me)

Source: garage door installer

Install garage door weatherstripping about 1/4 inch back from the edge of the opening.