Anyway, can we have Harry and Jessie every week? Like... permanently?
Well, Tom Cavanagh was listed in his usual series-regular spot here instead of as a guest star. Though there are some shows where recurring cast members get "regular" billing only in the episodes where they appear, so that may be the case here too.
Run, Jessie, Run! I don't know how she could've run at supersonic speeds wearing regular clothes/shoes. Didn't Barry have problems, in the beginning, with air friction causing his clothes to catch on fire?
That's something they tend to ignore most of the time. When Barry super-sped Iris to their new date site, her hair wasn't even messed up. And while Kara's clothes did catch fire when he sped her to the desert in
Supergirl: "Worlds Finest," he was later somehow able to bring her ice cream at superspeed without any melting. (Although the former case did involve him running exceptionally fast even for him.)
Magenta is almost an anagram for Magneto.

She has got to be the most powerful metahuman ever featured in the Arrow Universe if she could lift an entire tanker using her metal manipulation powers.
Weather Wizard is even more powerful. In the
Vixen season 2 premiere last week, he was shown attacking Monument Point with several tornadoes and a tsunami, which would require a staggering amount of energy. (I'm not sure how Weather Wizard could even summon a tsunami, since those are the result of seismic or volcanic events, not meteorological ones.)
And why is he assuming that if he gains meta powers, that it will be superspeed?
Because the dark-matter wave that hit him and Jesse wasn't just any old dark matter, it was from the experiment that recreated the accident that gave Barry his speed. Indeed, I got the impression that it was, in some way, Barry himself -- that when he vanished into the Speed Force, he passed through them along the way. At least, it was the same dark-matter surge that gave speed to both Barry and Jesse, so presumably it had some kind of a Speed Force component to it, and thus it's logical that the third person exposed to the same surge could also get speed from it.