If it is leaking, then very likely it is the cause of your popping noise. The leak will also continue to get worse (the escaping hot gases act like a cutting torch and erode the cast iron) and if you let it go long enough, ruin both head and manifold.
Unless it just happened to fall out (very unlikely IMO), any repair is going to involve removing the manifold and trying to get the broken end of the old stud out of the hole.
With the manifold out of the way, there are various techniques you can try. Personally, I have never had any luck at all using "Easy-Out" type extractors. For me, they usually snap off before the stud starts to turn, leaving you with a much worse problem! (The easy-out is much too hard to drill out.)
I have had fairly good luck with center-punching and drilling, starting at about half size and gradually stepping up until the threads just start to show on one side. (Impossible to get the center punch perfectly centered, so you're always off a little bit.) With care, you can then use a dental pick and tap to clean up the original threads. Or if not, install a Heli-coil.
What I plan to try next time is this:
https://bbs.homeshopmachinist.net/threads/54076-Removing-broken-stud-by-welding-on-nut
From what I've heard, the heat (and perhaps current) from the welding tend to loosen any rust, making it come out easier.
But since you are "not a mechanic", you'll probably want to take it to a shop instead.
FWIW, although not original, I've had a lot less trouble with those corner nuts after I started putting an extra heavy "setup" washer under the lockwasher. You can see the washer on the rear stud here