1) Sounds like the toothed plastic strip that is attached to the antenna is broken. You can pull out the antenna and open the motor assy to remove the broken strip. A new antenna can be fed in easily...there are aftermarket ones for $15. Read the directions to install it.
2) Do you hear anything when you first start the car? Electric motors running or hissing? If so, you may have an air leak in the system. If not, the compressor may be bad.
3) If it's like my '92 Camry's LED clock that fades in & out, yes it's somewhat common. But a warning that the sensor doesn't work means that either the ground is bad to that sensor or the sensor has gone bad.
I don't claim to know everything about this car, but these are the more common reasons for Toyotas in general.
Hope this helps!