Blinker DRL Ignition problems
The simple and obvious thing to try is to replace the LED bulbs with the original incandescent ones and see if the problems go away. That will demonstrate whether the problems are related to the bulbs or are a coincidence - it's not uncommon for things to happen after a change that look like they're related but really aren't. If the problems remain then we can work on diagnosing what is causing them without considering the bulbs. On the other hand, if the problems go away then we we can focus on what the bulbs are doing to cause these other symptoms.
BTW, are you 100% sure you got 3157 LED bulbs and not 3156? Installing 3156 single "filament" bulbs in sockets requiring 3157 dual "filament" bulbs can cause all sorts of weird problems involving current back feed and such.
When you say that the right turn signal is shorted to the parking lights, what are the symptoms which make you say that? Firebirds don't actually use the dim (parking) filament at the front unless the headlights are on. When the headlight switch is in the Off or P position, the bright (DRL) filament will still be active. If the right front lamp is always on and does not flash with the turn signals then you may have a stuck relay inside the DRL module.





