For me, maybe 2-8 hours max (or overnight if I am away for a few days)
Not sure what the reference point for Jot 2 is (if it runs cold) but "extremely toasty" does not sound normal. Mine is generally warm to the touch, but "extremely toasty" for me is Valhalla 2 w/o socket savers after running for an hour. If my Bifrost 2 started running as hot as Valhalla I'd be very concerned.
I do not think leaving it on 24/7 is detrimental to its lifespan. Multiple on/off cycles maybe moreso, kind of like how a car engine goes through most of its wear starting up.
I would like to think that as the capacitors "burn in" the sound improves, but that might be a bit subjective and don't know enough to make a solid argument one way or the other. I just enjoy it for what it is
Thanks for sharing, I will admit I have a bit of nervosa right now since I switched to running the BF2 using balanced out exclusively and am thinking of upgrading to Gungnir or Yggy. This might help cull some of that (ok, my wallet being empty is going to cull all of it, but still).