first with the antenna, these things get gunked up really easy, just have some one sit in the car, and turn the radio on and off while you spray some WD-40 on it. i took some, sprayed it on my hand and 'massaged' the antenna while it was up, then kept putting it down with the power button. keep doing this till it goes down by itself then wipe the excess off the paint.
now for the turn signal, when one of the bulbs is out then the turn signal will stay solid to indicate that one of the lights is out either on the tail lights or the front blinkers. so just replace the front bulb, although i suspect your socket up front is probably bad too. you can get a replacement socket from Autozone for pretty cheap.