Sorry but no you do not open the bleeder first; see
https://www.youtube.com/watch?v=qPwGcWi3gE0 for video on how to bleed although rather than use paper towels I prefer a bit of vinyl tubing over the bleeder running to a catch can.
The primer pump essentially pulls fuel from the tank and pressurizes the fuel filter, before you ask yes there is a check valve that keeps fuel from immediately running back into the tank. Cracking the bleeder screw releases that pressure by discharging whatever (air or fuel or a mixture) is at the top of the fuel filter head. So bleed as follows a) pump primer until firm; b) crack bleeder; c) close bleeder; d) repeat those 3 steps until all the air is out of the system.
If no fuel comes out when you crack the bleeder either a) the primer pump is not building pressure or b) the bleeder port is clogged. There has been at least one case of the primer pump check valve failing, in which case the pump never gets hard, and on case of the "O" ring or whatever that functions as a shaft seal on the primer pump failing, in which case fuel comes out around the primer pump shaft. I am not at all sure how or if the pump could fail in a manner where it would appear firm but not actually to have built pressure in the fuel filter head. The bleeder is identical to a brake bleeder; hollow inside/"V" shaped end matching and inverted "V" seat in the fuel filter head/small hole in the "V" thru which fuel runs when the bleeder is unscrewed. If that hole or the passage to the inverted "V" seat get gummed up the bleeder won't work until the passage(s) are cleared. Remove the bleeder screw and clear passage(s) with something like a pipe cleaner.
AC compressor cycles, even if AC switch is off, when the vent control is in the Floor only setting or in either of the 2 settings with the Defrost symbol although I don't think that would explain your unstable idle. If I have not said it before set the vent control to "O" for Off which should prevent the compressor from running at all and see if anything changes.
PS. I wonder if the primer pump check valve could fail in such a manner as to make the primer fail "hard" such that it won't pump fuel and if so doing could cause a weird idle. Way way out on a speculation limb here but could you rig a temporary filtered (just connect the inflow and outflow lines together with a basic cheap inline filter) bypass of the fuel filter head to run things long enough to see if the idle problem goes away? If it does replace the filter head.