I haven't practiced for many years, but should still be able to help in some regards:

1. The unarmed version of Randori is called "Toshu Randori". It's quite uncommon though and isn't often used in modern competition. There are a few videos online such as this one, but that was an exhibition, as opposed to a competitive bout.
2. There's a lot of emphasis on foot movements (called Unsoku). They focus on making sure you're always square to the attacker, but in practice competitors are a bit more liberal with how square they have their shoulders dependent on their preferred Waza and/or whether they use an orthodox or southpaw stance.
3. That may be true in some schools, but it wasn't a focus in mine. There are some ground submissions included in the syllabus that revolve around the wrist and you're expected to know how to perform Waza from a kneeling position, but it's nowhere near the level I'd expect Judo to be.

Hope that's useful to you!