Why would your brake lights and right turn signal not work and you have to turn the key half way to start the car in neutral so you will be able to change gears to drive on a 1992 Grand Marquis?

Check fuses, If brake lights do not work, transmission will not shift out of park. Brake light circuit is common to shift interlock. That's why you must step on brake to release interlock prior to shifting out of "Park" If stop lights are not working interlock will not release.