Omg, hi!! I'd love to see more spin-offs of Home, (and I definitely felt a sequel was needed for Do you feel at home in this place?), so I'll do my best to answer your questions! :)
I don't know if the magic system I used has a name, but this website gives a pretty good list of the types of witches I referenced and what they do! (I know notorphanedaccount took some creative liberties while choosing his character's witcheries, which I also don't mind!)
All young witches will be removed from regular society when their powers manifest, which can be indicated either by a mark or a small explosion of magic, such as in George's case (just to a lesser degree). This separation can include whisking young witches away from their families (usually when they're out of the public eye). This occurs on average around age 15, and never earlier than age 13. They are, however, allowed to visit their families once their training is over.
They're not supposed to talk about being witches, but they're not really bound to secrecy by a spell, so it'd make sense if a few persons or families learned about the witch world, so long as they keep quiet about it. If a higher-up (such as Sam) heard about any humans abusing the knowledge, he'd probably intervene and wipe some memories.
There is approximately 1 witch in every 100,000 people. In terms of love or close friendships, witches will form covens with other witches they're drawn to. It is not uncommon for witches to make friends with humans, but it's unlikely for them to become lovers with normal people because of how inconvenient it is, eg. most witches need to reside in magic-heavy surroundings to maintain their magic, but humans that're exposed to too much magic will feel negative side-effects.
I hope these answers are sufficient! For the topics I didn't address, they are outside the scope of Home, so I encourage you to explore the narrative within your own writing :) I can't wait to see what you come up with!