The interstage caps keep the first stage's plate voltage off of the second stage's grid. If the grid were higher voltage than the cathode the tube doesn't work well.
Yes, they are coupling caps. The name "interstage" gives you the answer to where they are.
They are in the signal path. But for some reason the final cap has more effect on the sound. I don't know why, I just accept it. Still I upgrade interstage caps, see below.
Since the plate of the first stage floats to the B+ at the output of the diodes at start-up they need to be high enough voltage. The RC time constant is different than the output cap and interstage caps are most often 1/10 the size, or less, of the output caps. Again, the signal goes through them and my first tweak on my Paramours was to change the interstage caps to KK Teflons.