New to me Parker 12ga.

[B. Dudley]

Up and down movement when closed is a loose lockup. Side to side is off face.

If it is loose lockup, the barrels will be away from the face and you will see light between barrels and breech face. Pull down on the barrels and see if you can see light still while applying pressure. If no light is visible, then you know it is just lockup that needs to be corrected. This could be corrected by replacing/refitting the bolt, or through a few other methods depending on who is doing the work and how they want to do it.

There is nothing wrong with doing the minimal work to make the gun shootable, and then doing just that... shooting it.
However, I kind of second Craigs statement on the subject. Bail and save up for a better gun and learn about what to look for. When VH 12g guns are the subject. Twice what you spent will buy you a good gun without any of the issues you currently have with this one. $1,000 - $1200 may seem like a lot, but in the Parker market (or even more generally speaking, the quality double market) it really isn't a lot.