Yes. It's ~10.5 hours to Jasper from here, then another couple down to Banff from there.
No, though I suppose you could fly into Calgary and drive from there.
Jasper National Park, Banff National Park, Yoho National Park, Kootenay National Park. Lake Louise, the town of Banff, uhm maybe other things that I'm 100% unaware of (likely lots of this).
Option 1: Go daycamping or backpacking through yonder woods.
Option 2: Find a hostel, room, or couch in the Lake Louise area and go exploring!
I'll likely have more valuable input at the end of this month.