First, welcome to the site.
Second, welcome to owning a drilling.
Addressing your issues more or less in order:
0. A couple pictures of your gun would have helped. That, and we like to look at guns....
1. Loose top lever. Does the top lever open the action or is your drilling one of those where the top lever is actually the selector between "shotgun" and "rifle"? If the latter, the top lever is not held in place by a spring and it will behave like you describe. If not, then a toplever spring is the first place to look. Yours might, or might not, be a standard size. If it is, you're in luck. If not, some craftsman with a file will have to take a standard size and work it to fit your gun.
2. Getting a new screw for your lock made is the textbook solution, if only because a proper job will include proper steel and hardening (if needed). Trying to substitute a screw from a gun contemporary to yours may, or may not, work. Your gun might be made with metric screws - diameter and threading/pitch - so using an American screw is not likely to fit properly. Not a big issue in a stock or something, but in the lockwork it is a big issue. Safety, you know.
3. Tang screws are not as difficult but, again, diameter and threading/pitch are issues. This, particularly in a back-action (or any hammergun) because they'll help govern alignment and thus function of all the other parts.
All that said, since the bores and lockup are good, the rest is fixable. You're going to have to get the oil out of the stock head anyway, so fixing the rest is something to do. Consider acraglassing the stock head once the oil's out.
Hunting season is closed for some months to come so it's not like you have to get the work done tomorrow. If you were asking me for suggestions, I would:
a. sell the other guns for the $500-600 you think they're worth and put that toward the drilling repairs;
b. spend only paper and throw your spare change into a bin, as a forced means of savings. This can easily add up to $500-600 per year;
c. get used to the idea that your gunsmith is going to be a person you see on a more-or-less regular basis, just like the mechanic for your car, so you want to connect with a good one who has a clue about drillings;
d. stick around here for advice from real experts;
e. learn to reload for the rifle (because just about every rifle caliber in a drilling is obscure, expensive or both);
f. remember that there there are no bargains, especially when it comes to drillings. If you paid less than $1k for a lot including a drilling and some other guns worth $500-600, what does that make the drilling worth?
Again, welcome!
