get a cheap DMM from sears or even harbor freight. test light works too, but it's more useful to have a meter.
as stated, see if there is voltage and ground at the fan connector with the AC on. if there is, the fan is bad. if not, locate the fan relay and see if it is coming on. if it's not, check voltage and ground at the relay control terminals. if that's good, it's the relay, if it's not, the PCM is probably not commanding the fan on.
the fan issue itself should not cause the idle issue. it'll cause the AC to be warm, as the high side will overpressurize, but this generally doesn't have much effect on engine idle other than the compressor cycles a lot more, which could cause a lot of variation but not poor running, unless the engine is just very sensitive to the increased load of the 250-300psi+ high side.
it seems odd that the AC is cold. it should be warm with the car stopped, if you feel the low side lines they might get a little cold but the high side lines will be scalding hot. with gauges, the system pressures will read like it is overpressurized, but it's just a lack of cooling of the high side which results in a low side that is unable to cope (causing warm evaporator/warm air from vents).
the car may have an additional fan for the AC on the front of the radiator. are you sure that no fan is running?