How Did He Who Must Not Be Named (Voldemort) Wind Up In Star Wars? (warning-spoiler alerts ahead)

I've just returned from seeing the new Star Wars film, watching the plot go gehunky-hunky-hunking along like one of the films many lumbering two-legged robots. Suddenly, mid-film, appears He Who Must Not Be Named. Giant-sized, and gone missing from the Harry Potter movies. What the heck is he doing in Star Wars? Do the villains of long-running film series hop from franchise to franchise? Or do they just all have to have no noses?

Afterwards, my family and the two clerks at the Walgreen's counter were trying to figure out the gaping holes in the plot, particularly those having to do with young Snape (Adam Driver). I can find the answers on-line, and even ideas of how future plots will run, but I can't quite figure out how He Who Must Not Be Named (called Snoke in this iteration, a combination of Snape and Smoke?) saves his protege mini-Snape from the total collapse of a planet not to mention falling into a pit of lava after getting shot with a compound bow and taking several hits with a light saber than can take down trees.

And by the way, foresters of the world, unite in protest! Those were pretty big trees they were chopping down like firewood.

Oh, wait, I forgot. After that, the whole planet goes up in fire and smoke.