I have a 95 Mercury Grand Marquis. It's makes a loud squeaking noise when I turn. What could this be?

Dry tie rod end or Ball joint.

maybe power steering pump?

check your fluid

Perhaps ur front suspension has dried out & needs lubrication. Most auto parts stores sell the correct product to lube the bushings.
You can do the lubrication or if u have u oil changed at one of the Oil change stations be sure & have them Lub all the zerts & while he is under the car taking out the filter & old oil ask them to spray all the bushings. l provide the lube to the service tech & pay him a little extra for his effort.
l think this will stop ur squeaking problem.

Best wishes
jerry

that is common for that car it is the ball joint or tie rod possibly both there r no zerk fittings to regrease then so they dry out. it more than likely wont be the power steering pump cause it will make a whinning noise.