I've tried the soldering iron with the copper tube attached & that works great, but the only problem I had was finding copper tubing small enough to make the rivets semi scale in size. Also, I'd like to do screws in places. Any helps appreciated

Try a brass T fiting.
Scott

I've never attempted to do what you are attempting but I have some thoughts about how you can create the screw head. I would start with the method you are using to create the rivets and then come back with a blade shaped tool, fitted to your soldering iron, to create the screw slot.

To burn the Slot of Screws as well as the Srews at the same time, insert or jam a small width strip of brass or copper sheet (shim material)into the end of tube; the strip or sliver should be the width of the inside diameter of the tubing you are using, the effect would be the creation of a circle with a slot across it immitating a screw head when etched or burned into the paint/primer.

You can go to a VET supply outlet and buy several sizes of hypo needles, some so small you won't use. These can be cut down with a dremel cutoff wheel, because they are made of stainless steel they will last forever and you can sharpen them with a file. they are of course shaped to a very sharp point and that is why you cut the point off with a dremel tool.
To make screw heads you can buy a cheap (quality) set of mini screwdrivers and cut the tip off and insert into a piece of tube and use that for the screw heads, file the (x) down just a little to flatten it out and allow the tube to also contact the surface.
Good luck

Kelly, Your method is right on. I'v done that very thing with the exception of leaving the small screwdriver point protruded a bit to give a deeper and more realistic effect. Does take a smite longer to burn but worth the extra.