The scale on that map is tricky...the river is too wide for the mountains or vice-versa. The mountain size makes me think around 800-1000 miles but the river and forest makes me think 200-400 miles. I'm all for artistic exaggeration but some aren't. If I had to make a call then I'd put it in the middle and say 500-700

There are rules and there are generalities for where forests are. I don't the know the rules so I'll stick to generalities...no water = no forest and really big mountains block rain. It's your map and if you want a forest somewhere in that desert then I'd put an oasis there.

Snow is pretty much the same but with the added dimension of hot/cold. Rain + cold = snow. Hot/cold is also affected by height...higher = colder. So if you want some snow on your mountains then I'd put it in.

Floating islands would best be indicated with a drop shadow that has a big distance. Drop shadows are great at making things look like they're floating.