1

March, April, May and November are the less busy times which i think is more important than good weather seeing as it rains most days in the mountains anyway. I had a group to myself in Rwanda in May (downpour for the entire trip though but the gorillas were pretty cool still)

2

I went in dry season (Aug) in Uganda and had no rain.

You'll have the same number of people in your group no matter whether it's busy season or not, so I'd rather go when there's more chance of dry weather- so June-Sept, Jan or Feb. You'll have more trouble gettting permits for the busy time but it should be fine if you plan ahead.

3

they don't pack people all into one group if its less busy, they are pretty good with putting you in a small group if you wish. i've been a few times in Rwanda and never had more than 2 people in my group despite other groups having 5 or 7 people in and me being alone. It depends which group you want to see. if there are a bunch of seniors who want a short trek and you want to go an trek Umubano or Susa groups, you'll do it alone/in a smaller group.

In Uganda you book your group in advance so if you book H group for example and 7 people book R group, you'll still see H group alone.