Need to pinpoint which corner the squeek is coming from and then inspect it. Soft, spongy pedal can occur after new brakes put on due to the following: When your brakes are normally used, think about how far the pedal travels. Usually it's about a quarter of the way to half right? your master cylinder is just what it is.. it is a master.. cylinder. keyword: cylinder. where am i getting.. you don't press the cylinder beyond more than half way all it's life under normal use.. the unused part of the master cylinder collects corrosion and contaminates on the cylinder lining. Then when you compress your calipers to fit new pads and/or bleed the brakes, your pedal then becomes capable of traveling 100% to the floor. This is when your master cylinder becomes damaged because the seal gets messed up. When you bleed brakes, or replace pads etc.. whenever you are capable of pressing the pedal to the floor you shouldn't do it because of this. instead, press the pedal down no more than 1/2 the way and let up and press again over and over till you feel pedal firm up.
Also if your rear shoes are not adjusted properly, your rear brakes can and will likely act up like you describe. Your e-brake applied the rear brakes mind you.. so you can also differentiate the problem to the front or rear by whether the noise happens when you use the e-brake. your shoes should be adjusted so that they are just rubbing lightly on the drum. Drums having a lip will make it harder to adjust properly. good luck