Installing an IGH in a Trek District SSB
Checked with Trek, and that is a 135mm spaced frame, so yes, that hub should work fine with it.  I would make sure of the interface for the belt drive "cog" on the rear wheel, make sure it will work with that hub.  Otherwise, that Alfine should be very good.  That shifter should work fine with that hub too.  Making that interface question the only issue I see other than building the wheel if that's your plan.  If you've never done it before, be aware it's a lot more involved than it appears.