The fae aren't exactly helicopter parents; the Adopted get a fair amount of freedom, which can include starting up their own little side hustle. While it's at the "hobby tier" they likely wouldn't even make note of it, but once it becomes a proper speakeasy sort of business, expect their court ruler to make note of what their Adopted is doing. Their reaction could be anything from "I want a cut" to "Stop it" depending on which court ruler we're talking about exactly. (The NPCs at the pub would absolutely be interested in getting some more unique liquors, however, so once it becomes more common knowledge, they'd likely stop by for a sample/to buy a bottle.)

For alcohol specifically, you're right that the ingredients are the main thing, and fairly easy to obtain at the market/from their fellow Adopted. As for a place to own for such an endeavor, yes, they'd need to talk to their court ruler, but they're hardly looking for a business plan; feel free to lie about the building/land's true purpose.