The hum may be a local problem only, and not radiated.
Have you had a local ham listen to verify that the hum
is present? A nearby receiver may hear "hum" that is
caused by RF being carried on the AC line.

The chirp could be caused by poor supply regulation,
or it could be related to the transmitter. Does the
chirp exist when the VFO is run barefoot, without the
transmitter?

Pete