I worked through all that when I had a manual three-way valve balancing between skimmer and vac. I never could get the balance right, so I couldn't run the vac all the time. With both running, I couldn't get good performance out of either. So I added an actuator and use my automation to switch modes and ramp up my VS pump to optimize each function.
Run times and RPMs come down to how they work in your particular pool. I don't think there are any hard and fast rules. There will be a set RPM to optimize the vacuum, if you have a VS pump. Mine came with a gauge that attaches to the hose to determine if the amount of suction is correct. You can adjust that suction using RPMs, the valve(s), or a gizmo that sometimes comes with the vacuum that sets the flow (mine didn't come with that, but I think it gets installed between the hose and the vacuum port). Other than setting vac flow correctly, the rest is based on what your pool needs. Leaves on the bottom, more vac time. Leaves on the surface, more skimmer time (or higher RPMs), etc. You just have to keep adjusting until your pool is as clean as is acceptable to you, within the limit of what you're willing to spend (pump time + RPMs = electric bill).
But the real reason I'm chiming in: don't forget that the vacuum port and the end of the vacuum hose, under certain conditions, can be exposed suction, which can be dangerous. The vacuum port needs to have a proper safety flap. And while the vacuum head is some protection for the end of the hose, those hoses come apart relatively easily, which could make dangerous suction exposed to an inquisitive person. Evisceration does happen in pools, along with entrapment. So...
You should never set the valve(s) to 100% suction for the vacuum. The skimmer port is less of an issue, because it is well protected inside the skimmer, under the basket. But the vacuum port, and the end of the vacuum hose, is very much "in your pool." I'm still working this out, but my logic about it is: adjust the valve that controls the balance such that it can never be turned to 100% suction to the vac. By allowing some amount of the suction to come from both the skimmer and the vac, if the vac port or hose gets exposed to a person, then the suction against the skin is relieved through the skimmer port. I'm still working out what a safe balance is, 10-90, 20-80, 40-60? I honestly don't know, and don't know how to determine that. I'm going to lock down my actuator to some split that still allows the vac to function well, but diverts as much suction as possible to the skimmer. The closer to 50-50 the better, I think.
Once I figure out a good split, I'm going to hold something up to the vac port (NOT MY HAND! At least not a first.) and see what happens. Not sure what to use. A rubber ball? A piece of fruit? Dunno. Something that would simulate a kid's belly, frankly. That, after all, is what you're safeguarding...
The other safeguard I employ is to run the vac mode only in the middle of the night, when nobody is in the pool. During the day, suction at the vac port is always 0%.