If you look at the OP's first photo, I see two potential serious issues.
- There is a hole in the steel where the dropout is brazed onto the fork blades. I can't account for that hole, but it could mean a poor brazing problem.
- The dropout itself is deeply worn. It should have a single curve, and it appears to have a double curve where the wheel was resting. There is also a lip worn where the end of the axle would rest. That may not be a critical problem, but it means something is seriously wrong with the wheel installation.
Then looking at the third photo, the threads on the front axle are completely worn away. It could be difficult to service the hub in the future, but is wearing to the point that the OP could be losing axle.
The first question I would ask the OP is how he is locking the wheel on the bike. The proper way is to screw the quick release down until it touches the dropouts, then flip the lever so that it is about as tight as one can flip the lever which locks the wheel in place. Typically the lever is oriented either straight back, or along the fork blades.
Likewise, on the rear, orient the rear lever either straight back, or between inside the dropout triangle, again locked in place by flipping the lever at a point where it is close to as tight as you can get it (not too tight as to necessitate tools to flip it back).
DON'T USE THE QUICK RELEASE LEVERS AS WINGNUTS.
As far as what I'd do with that fork? I don't know. Did you buy the bike new? With a warranty? I'd argue that the hole in the dropout may be a sign of a manufacturing defect. Perhaps the manufacturer put putty in it, and it fell out. So, I'd see if I could get a warranty replacement.
It would only take a few seconds for someone who could braze to fill that hole.
You still have the worn dropout problem. It is probably OK, if the QR skewer is fitting properly in place, and not being held out of place by a ridge or lip or something. But, get your skewer TIGHT.
Oh, also that lip that has worn around the end of the axle could prevent proper tightening, and might need to be removed with a round file.
A wheel wobble once everything is locked down could mean a wheel out of true, or broken spokes. Or even a bent rim. That could exacerbate the wear problem at the dropouts. It is easy enough to true a wheel, given a spoke wrench. But, you can also have a bike shop look at it, as it is also easy to make a bigger mess.
Oh, also a wobble without spinning the wheel can mean worn bearings/cones. Your battered axle may make fixing that difficult. But, you might be able to tighten the cones and locknut even in the current condition if needed, but if it is badly worn, then it may also be completely toast.