The ticking noise is probably amplified from the supply line. Try running the 386 from a separate supply on your breadboard and see if it eradicates it. Either that, or it's the PIC program polling the port you've got the Audio connected to, put a scope on the Audio line and see if it's clean or if you've got a pulse on it.

If it's just a Doorbell or Alarm, then the Audio Amp probably wouldn't warrant it's own regulator as long as your supply doesn't exceed it's maximum rating.

As for the LCD. It's 5v Supply can be the same as that for the PIC because it draws minimum current at best, but the exception is the BACKLIGHT for any LCD. I tend to supply that seperately because unless you've got one of the new style white LED sort, the LED array is usually very power hungry. Even then I rarely regulate it to any extent. The exception being if you have a supply line which is going to vary considerably under load (eg lots of Relays switching on and off), then if the Backlight isn't regulated, you'll notice a change in the light levels as the unregulated supply goes up and down under differing loads.