Yes, scooping would be your action, using a potion even on someone else is still a use action. So you're good.
Alice will wake up, she doesn't need a ration, officially that will do nothing, and no, feeding Ashley to Alice wouldn't be helpful.
Alice will have her turn immediately which is of course to take out her anti-human racism on Ashley, triggering the scripted event that forever opens the gates to hell... uh, I mean, getting whatever the mechatherial goddess will do to happen. Seems fair.
>no level 2 spell slot
Of course a focus doesn't need a spell slot to trigger a spell, you don't even need any MP left at all, it's just riskier and less powerful as it needs to use its MP to completely get there.
As you saw, with a lvl 2 slot you got a 3.75 level spell, with only a lvl 1 slot, you have infinitely many of these as long as you have MP yourself, the gem will cast a 3.25 level spell. If you had no MP left at all, the 6MP gem would cast a 3rd lvl spell even. I will handle the math.
It's less efficient but also riskier in ways you really don't need to worry about only that it is riskier. If you want the breakdown I can provide it.
I suggest you don't need to throw it, that was something we learned already. I also suggest you shouldn't pick an AOE spell if there is one that has a higher damage potential specifically for a single target if it exists, even a cantrip.
I also suggest you don't use a spell with a spell attack because his AC is high and you have a poorer chance of hitting that, but I could calculate the odds for you if you have a couple options in mind.