Air conditioning issues/observations

[ScottAZ]

Hi all, my new to me 02 S has been great, but the AC seems a little weird. In full disclosure, I'm in Phoenix and it's been above 110F for quite some time now, so we're talking about extreme conditions. Here are my observations:

When the compressor is on, it makes a surging sound. Sort of a slow low to high sound in the background. There is no variance in the engine revs in correlation with this surging sound.

Above 3K RPM or so, the compressor seems to shut off and I'll get blast of warm air after a hard acceleration. A noticeable whoosh sound is present once the acceleration has leveled off and the air blows cold again.

The AC is much colder when the car is at cruising speed than when idling, even when just stopping at a red light after the car is fully warmed (cooled) up. At cruising speed, it's nice and cold, but when puttering around in stop and go traffic, it's warmer.

In our extreme heat, the AC is barely passable. I understand a black soft top is hardly ideal at rejecting heat, but given that the cabin is so small, I'd expect it to be able to cool it easily. Maybe I'm asking too much of a 16 year old car in the insanely hot desert. Are any of my observations out of the norm? Thanks!