Also, what is the deal with the SOS only thing I see for Pokemon like Pikachu?
I've been looking into how SOS battles work, so here's what I know:
SOS-exclusive Pokémon like Happiny and Pikachu only show up when a wild Pokémon calls for help, and for regular SOS battles, the Pokémon called in is tied to the species of the wild Pokémon. In Pikachu's case, they will appear only if your initial encounter is Pichu. Even then, it's not guaranteed, and you may find another Pichu instead.
Basically, if you look at the Pokéarth section of this site, you'll see a grid of Pokémon. Route 1 is a good example, as there are many rows and many columns. The topmost row is the wild Pokémon you'll find just walking around in the tall grass. If that wild Pokémon calls for help, it will summon a Pokémon from the column that Pokémon is in. To get an SOS-only Pokémon, find that Pokémon on the list and go to the top of the column, and that will be the wild Pokémon you want to encounter. Use an Adrenaline Orb, if you have one, and eventually, if you just let the wild Pokémon keep calling for help, it'll eventually call over one of those.
Currently, I'm doing SOS battles under weather conditions and trying to see how I can get Hidden Abilities from them. Right now, I'm having very little luck, so there's probably something I'm missing. To anybody who knows more about SOS battling than me, how rare are Pokémon with Hidden Abilities? (I've been attempting it and have not found even one. I just now tried my hand at Alolan Vulpix and kept the chain going for so long, Vulpix ran out of moves and had to use Struggle. Must've fought at least 30 or 40 allied Vulpixes. None had Snow Warning.) And to initiate a weather-based one, do you just simply find any wild Pokémon when that weather condition is happening?