April is too early, there will be snow on the ground and average temps are below zero. Most facilities are closed or unmanned until June.
The only English-language map I'm aware of is in Lonely Planet's Hiking in Japan, and it's not very detailed. Sapporo has lots of hiking equipment stores, Shugakuso is well-regarded by serious hikers.
Everytrail has a selection of GPS tracks for the park.
Yes, you can reach all main trailheads with buses, just check the schedules carefully. Basic guidance here.
Depends entirely on the weather. If it's a clear sunny day, no problem. If it's foggy or a blizzard rolls in, big problem. On average 5 people a year die in the park.