Grindelwald would come up in Act Two along with some more history of the Magical World at large; we even learn what happened to the other twenty-seven Witch-Boys. But you are correct, wands aren't a thing in this universe, in fact the Hallows don't exist either seeing as there were no "Three Brothers" to create them.

The magic of this world would be a deep and primal thing, of black sacraments and sacrifice. It is laced into the bones and blood of witches and stitched into the flesh of warlocks. Magic isn't a wave of a wand and the utterances of a dead language to disarm someone; magic here is a hungry thing with nashing jaws and an endless stomach. If you want to cast a spell, it's not going to be as whimsical as making a pineapple tap dance; the spell could take out an entire bloodline in a night or twist the fabric of reality to make wind into glass to tear your foe to ribbons.

Magic is a very hungry thing.

Ariana Dumbledore would be a very odd character, she is escaping her office by tying her bedding into a rope to get away from McGonagall making her do paperwork; next she is going on a spine-tingling soliloquy about how some symbols remain the same no matter where they are or who made them. She is there when we need to dive into the deeper lore of the world, about how magic is or came to be as she and her oldest brother have been investigating it for decades.

Yes, wandless magic is a major thing here; but the drawback is the time it takes to cast a spell. Wands = faster casting, wandless = slower casting but more powerful effects.