Note that it is very important that you stop every 15-20 rivets and clear the tip of residue. Areas with primer coverage will tend to melt up into the brass tube and clog the tip quite frequently, so just clean it out with the tip of an X-acto knife and scuff the outer surface of the tubes with a sanding sponge or sandpaper to keep the outside clean.
Once you have applied all the rivets to an area, you'll find that the heavier primer areas can tend to have a "flange" of paint melt and stick up around the edges. I level all my rivet edges down to the same relief by hitting the whole area lightly with a medium grit sanding sponge. Then, I follow up with a fine grit waffle sponge to smooth out any sanding scratches.
Once you've done this sanding, the primer dust will plug up the rivet relief on the plane, so I just take an air gun on my air compressor and blow out all the rivet rings to clear them out of any sanding dust. Otherwise the paint will plug up with the dust filling any relief and hide all your work.
For larger slot-head style fasteners, I use the same technique with a larger diameter brass tube and one other modification. I take a thin sliver of brass and slide it down inside of the tube to make the "slot" feature. This burns the ring and the slot all in one pass.
As for raised/dome-head rivets and screws, I use a hypo bottle with some water based glue in it to place small droplets of glue down on the surface. When they dry, you get a pretty decent pan head or dome head fastener. Many different glues will work for this, but I generally use Elmer's white glue with a little Titebond mixed in and thinned with water. The water is only so that it will be thin enough to pass through the needle of the bottle.