How does the speed/amount of mantle material rising and sinking and the way that mantle material moves the plates affect a plate’s speed?

Think of the ocean or any other large body of water. There are a lot of things going on. Hot spots, different densities, plumbs rising and falling within the body of water.

Now, let’s put a large comparably thin material floating on top. Think of ice sheets in the arctic or antarctic. Ice sheets can flow along with a current if too many different stresses are occurring the ice sheet tend to rip apart or fracture. When the ice sheet encounters another ice sheet they may separate, grind past each other while tearing off pieces or they slowly mash into each other piling up chucks of ice until you have hills are larger.

If it’s thin you get pools of liquid water, if it’s thick you have a very stable base.

Back to your speed question. Yes, all of these things add or take away from the speed, but you are applying forces to such a large object that it moves quite slow or immediately breaks up under the stresses.