An important factor in muscle building is tempo, more so how much time is dedicated to the eccentric/lowering portion of the lift. I can look up the studies but eccentric contractions are more effective and pertinent to the muscle building process. As far as strength and power and how they effect mass, it's subjective. There are some small powerful guys and there are some large powerful guys. Being strong and powerful usually equate to a higher level of athletic ability, so generally the stronger and more powerful you are the more muscles you could be. But again its subjective.
At the end of the day strength is just a number you can slap on as a limit but power refers to how quickly you can move that number. I was going to look for two different videos to link but this one shows what I wanted to.
YouTube - Spencer Wallace (600 Pound Squats) ( Feb. 2010) His first 4 lifts he completes the lifting portion of his squat in about 1-1.5 seconds on his last rep it takes him a little over 2 seconds. If all the lifts were performed by five different lifters you could easily say they are all strong, having the ability to squat 600 pounds, but you could also say the first lift represents a more powerful lifter than the last lift because it moves 600 pound the quickest.
Explosive movements will still work the stabilization muscles. A benchpress performed correctly is essentially a full body movement. You might hear from body builders that you need to press a weight slowly and controlled to feel the burn or some other form of broscience. But someone performing a quick, explosive movement that has proper form is still under control. Performing a movement explosively will train your body to do just that, push a weight explosively. Without getting too much into it, there is a finite limit of time under tension with regard eccentric and concentric contraction that a body can sustain under a certain period of time. The ability for eccentric contraction is superior to that of concentric contraction, so the more powerful you are the more time you could spend in eccentric contraction, if you chose to.
A good powerlifting routine will utilize accesory work to bring up lagging muscles along a particular chain to help to strengthen a main lift, that's correct.
