1) what do you mean by "HD radio"? the power antenna motor kicks in when the stock head unit tells it to. did the motor stop working when the radio was installed? if so this "HD radio" may not have been installed correctly and wont tell the motor to turn on. The head unit controls a relay that turns on the motor. listen for a 'click' when the antenna should go up. if you dont hear anything, the 'antenna remote wire' (usually blue) is hooked up wrong, the relay is unplugged or the relay is toast. if you hear a click but the motor doesnt run, the motor is probably burnt
had a JVC High Def radio installed at circuit city. If I remember correctly, I stopped hearing the motor before having the radio installed.
2)if you find out the motor is still ok, take the wheel well apart, take out the antenna motor, take the cover off, remove the broken gear strip, put it back together and back in the wheel well, then feed in the new antenna/gear strip as described in the writeup.
3)if the motor is no good or you ditch the stupid thing anyway, buy a toyota OEM whip antenna assembly, remove the motor assembly, cut the wire off the motor, install the new whip antenna base, TAPE THE WHIP ANTENNA WIRE TO THE CUT END OF THE OLD WIRE TO PULL IT THROUGH THE FIREWALL, then plug the new wire into the head unit and screw in the mast.
I'll listen again, but I don't think I hear anything. I may go ahead and try what you suggested in number 3
4)no, the plastic piece does not affect the reception, but you will not get very good reception by just pushing the busted mast back in. the whip antennas get way better reception anyway.
5)as for that antenna from antennax.com, it says right on the website:
"PLEASE NOTE: This antenna DOES NOT replace power antennas OR roof / windshield mounted antennas."
the one on that website that does replace the power antenna has the signal wire that has to be hooked up to the head unit. it is better to just get the standard whip antenna from the dealership, because it includes the rubber seat and it bolts right to the same bracket the power unit does. then if you still want a rubber one you can unscrew the metal mast and screw in the rubber one.
also, i am just going by what i know from my 2nd gen so i am assuming yours is similar. this writeup was performed on a second gen as well. anybody feel free to correct me.