SCREW LENGTH

To answer your question as to how many threads must engage to be sufficient, You can do a quick google search on “screw thread engagement” and it will yield a lot of info.

First note that screws and bolts aren't the same as far as thread engagement. Screws engage one half of the joint being developed. Bolts pull two or more pieces together. In critical situations like head bolts on an engine, the bolts are torqued to stretch them slightly with a static force that is less than the dynamic force applied when the cylinder fires. That way the bolt never moves and stress failure is reduced. There is a pretty standard formula for figuring how many threads are needed to engage to make an acceptable joint. It is long and complicated. And things like tensile strength of materials and design loads come into play.

One of the design goals for a screw joint is to have an amount of thread engagement so that the screw shears in tension before the threads strip in the hole. A good general rule if both thread and hole material are of equal strength is the minimum thread engagement length should equal at least one time the full diameter of the screw. So, if you had a .125” dia. screw, the thread engagement should be at least 1/8".

For a blind hole such as mounting a sight onto a barrel, I always figgered that a minimum of 4 threads in a 6-48 screw hole was a barely acceptable. As far as I know the sights I put on using that criteria stayed on. For a screw going into a receiver ring, I'd size the screw length so that the end of the screw is just flush on the bottom side of the hole. That's as good as it can get.

It should be noted that a little dab of grease or wax on the screw will significantly increase the clamping pressure of the screw joint. Here's something I found that explains it quite well.

Torque/Tension Rules of Thumb

Most of the applied torque is NOT used  to general tension in the joint; it is generally consumed follows:
    35% overcomes thread friction
    55% overcomes under head friction
    10% created clamp or tension
Friction plays a significant role in the torque/tension relationship.  Changes, which appear to be small (adding wax to the bolt), can have significant effect. A 10% reduction in friction can create a 25% increase in tension.
Torque to approximately 70% of yield strength (for hard joints).

Myself, I wouldn't complain about the length of the supplied screws. As long as they are long enough to cover the application it should be the installers responsibility to size them for length for whatever hole they go into. One can't realistically expect them to have just the right length for your particular application. That's asking an awful lot from them.

Tom