That fitting can likely be tightened down SLIGHTLY, and that will
control the "drip." There is packing under that bonnet. This is a
common problem. As to the other fitting, it is a bleed cap, used to get
air out of the system. You might want to replace the packing... small
packages in the plumbing department. Either the graphite or teflon
types work fine. Handy stuff to have around for just his sort of thing.
It looks like little pieces of string. Just wrap it around the valve
stem, and put the bonnet back on. It is easier if you remove the valve
HOWEVER, that valve seems pretty corroded. I would give serious thought
to putting in a new valve. They are cheap enough. Of course, pull the
new valve apart before you solder, so as to avoid destroying the seals.