Our 2005 Buick LeSabre Custom has had intermittent operating failure with the Heater/AC fan switch (all speeds). Now it doesn't work at all. Is it commonly a fuse, or does something in the system give trouble? Where is the fuse for it?

if intermittent then most likley not a fuse - if there's power to the switch then i would suspect the switch.

Now the switch does not work at all. I seemed to see online, with the Buicks, that there sometimes is a failure in contacts with the fan motor, or somewhere in the system. I'm not sure how to chase this down.

Switch just worked for AC, but fan motor seems slower than normal and smell of burning (rubber?) started. Turned it off. Is this the fan motor?

Check the fan motor and it's connections. Turn the blower (fan) on and wiggle the fan connection to see if it effects the blower's operation. Check the connection (with either a test light or a digital multimeter)to the fan to see if it has power to if at the various settings of the climate control. If no effect, hook the blower to battery voltage and an alternative ground to see if it works now (should work at full speed). If not replace the blower (fan)motor.

The fuse in under the back seat cusion. Fuse number 2. I have the same problem. Some times works if I move the blower slide switch back and forth very fast.