#1
I just measured it: the action at the first fret is a hair under 1/32". Action at the 12th fret (no capo) is 1/8" for the low E. About the same (a hair less so that the top of the string sits at 1/8") for the high E. It looks to me that the nut is cut OK, but the bridge/saddle is too high, isn't it?

It's strung with John Pearse 600L strings and I find it very difficult to play. Like, very. Finger slides are a bitch. By comparison I have 10/52s on one of my electrics and I have absolutely no problem playing it...

FWIW it's a resonator, so maybe it was setup that way to play slide and not finger style. But it means I'm not comfortable to set it up myself and would probably take it to a qualified tech.
#2
Is it a square neck or a round neck? If it's a square it is meant to be played slide. Otherwise, it is probably the action. Check the shape of the neck.
#3
It's a round neck. I wouldn't be doing finger slides or trying to play finger style on a square neck. ;-)