Heater/air con heater only works on no4 speed&air con button works but because fan doesnt work on 1.2.3 settings air con not blowing . if you press circulate button air con goes off ,and circulation works

Isn't your heater supposed to blow hot air?

if you saying the fan wont blow it may need a fan motor not uncommon it might be a speed switch if it has one some time you can hook a wire on the back of the speed switch plug in to get it on high use a 14 gauge wire or bigger a small jumper bent in a loop with the rubber peeled off the ends and shove them in the switch plug find the 12 volt ht wire on the plug with light or vom then try the other wires one at a time til fan runs with ignition switch on

blocked air flow

This is typical of a voltage resistor pack problem, it controls the different speeds of the fan.
I'm not familier with your Tahoe, but this is usually installed right in the air stream of the fan to keep it cool.
Look for a connector block with 3 or four wires, installed under the dash of passenger side, right ito the air tube moulding, very close to the fan.. 2 or 3 screws, should be quite easy to replace it and inexpensive. Just be sure to install the new one all the way before trying to turn on fan. It needs the blowing air to cool or may burn out immediatly.

a couple of things,1 blower motor fuse.2 blower motor gone out.3 switch on fan speed control switch not sending signal to fans.after checking the fuses.next check theswitch on control panel.set ac or heater.if fan still doesnt come on then replace it.when it work and then stops working there are a lot of possiblities that caused the prob relay too not fliping over inside staying close loop.hope this helps.

the blower motor has no affect on the AC system,
start the engine and turn on AC and watch the AC compressor to see if clutch engages,if it doesn't the system isn't full,if you are correct the clutch should be engaged and should quit when you change heater speeds,

you most likely have a bad airmix servo. this happens alot on these. they are expensive to replace too.

replace the blower speed control resistor, they short and allow this to happen

Replace the temp control on this car, it should be electrical control not cables.

When you find the fuse if it has blown also check the resistor to control the fan speed. I cant remember if the 1 series has a load resistor multi tap but it may have failed if you use 1 or 2 speed on the fan a lot, max will bypass the load resistor where as 1 will use maximum load and the thermal fuse might have blown. But replace it as caution. In the earlier models it had a block which was nicknamed the hedgehog, a load resistor buried under passenger foot-well up toward the centre, loads of spiky aluminum pegs which cold air blew over to cool it, always packing up in the earlier models £25 from scrap dealer cheap fix compared to the £££££££ BMW dealers rip off. Heater or air con would either not work or blow erratically. Hope this helps