Yea, I am not surprised this failed. You need to nail this, all of it, not just where it is popping off the wall, everywhere. 18 gauge brad nails, use a paintable wood filler to fill the holes, sand, then paint, you will not see any nail holes.

Pin nailers work well, but don't buy a pinner just for this.

For future reference, in certain applications, just gluing things works well. This is not one of them, you still need to mechanical fastening.

It is not necessarily poor workmanship. Things may have settled or warped a little over time. It is just how wood and buildings are.

Your reveals do look tight in the photos. Measure the door, measure the frame. Door should be 1/4" less. If it is less, than you should trim the doors. If you don't have the tools or the skill, contact a cabinet maker to rip these down. They should charge you no more than $100.

Its a compressive hollow wall anchor. There is nothing exactly special about it. There are many wall anchors with similar or superior performance. I agree that there are wall anchors that are much worse, but that does not mean the a duopower anchor is the only acceptable one to use.

Looking at the other post you got some reasonably good advice but your problem is still not solved.

Can you measure the interior dimension of the frame and exterior dimension of the wood for me? The frame should be 1/4" larger than the door. I guess it is possible the multiple layers of paint over the years have caused this to be closer to 1/8" or 3/16", it looks a little tight in the picture. It may need to be cut down a a smidge just to make everything work again.

If it is the right dimensions then its really tough to give good advice without getting my hands on things. Reasonably as long as you have a 1/8" reveal all around and the correct hinges you should be able to adjust them so they function appropriately. Did you mount the new hinges following the instructions of the new hinges or in the same mounting position as the old? they may not be directly equivilant in all respects.

This is what you want to use. Or something like it.

You want to shim the mounting bracket under an mounting screw holes where it is not touching the wall. You can use regular wood shims available at any hardware store. You will want to drill to drill a pilot hole through the shim and stud to stop it from splitting. Use a utility blade (always cut away from yourself) to score the and snap off shim when done.

It is likely just a masonry wall. Impossible to tell from the photo. Just use an appropriate wall anchor. Always be careful when drilling holes in walls, if you do not know where your services be extra cautious. Hitting plumbing or electrical will ruin your day/week.