45 studs will be too weak. 70 studs is the minimum if you have chipboard.
You should preferably have 45x95 if you are using plasterboard.
Important for good soundproofing is to, for example, offset the studs with insulation in between. So that you don't have wood contact between the two rooms.
Something like this:
X X X
X X
Optimally, I think 45x95 with chipboard or OSB and plasterboard on the outside would work best.
Then I think you can sleep soundly!
Epdm is a bit overkill.