It’s more normal to see the screws on those ABR-style Tune-O-Matics pointing forwards in order to stop the strings catching on the intonation screw heads. Otherwise you need to have a shallow string break angle so they don’t touch the screws as they will vibrate and buzz and erode the screws (and the rear edge of the bridge) if they do. I’ve seen this happen on a couple of guitars. You want a reasonable break angle to stop string buzz in the saddles and you don’t want the stop tailpiece set too high either. The lower the better is the general consensus (which is why you sometimes see the strings fitted backwards and run over the top of the tailpiece so that the tailpiece can be screwed right down to the body.

On the Nashville Tune-O-Matic style bridges, the design sets the intonation screws lower down so they aren’t in the string path, so these are normally seen with the screws pointing backwards. Also done because with the screws lower, they are harder to get to with the bridge pickup in the way.

The screw retention spring can be loose and buzz, though often this is because it’s not fully inserted into the two locating holes fully. You can also adjust the spring with pliers so that it sits more tightly against the screws.

The kit T-O-M bridge saddles can be quite loose in their slots, which itself can cause string buzz issues. A good quality bridge will have almost no side-to-side play in the saddles. If this is an issue, then bridge replacement is best. You don’t need to go for anything too expensive if you don’t want to, as you can get Korean-made low cost good quality replacements. Also look for metric versions, as the direct Gibson replacements will be imperial with different post spacings.