When braking it seems that my pedal goes down too much. It stops OK in normal conditions. If I pump the pedal twice it does not go down as far on the second press and seems to stop better. Without double pressing and going down a steep hill, I can get the pedal to bottom out and it sometimes does not fully stop the car. Pads and rotors seems to be in decent condition but are probably old. Could my symptoms be a result of old brake fluid with air, or do I have a problem with the master cylinder?

 

"pumping up the brakes" is a classic indicator of air in the lines. Could it be the MC? Yep, could be how the air is getting in the lines. First step with a soft pedal is to properly, thoroughly bleed the system. Then monitor their condition. Does the problem come back or are you good now? If it comes back you have to start sleuthing. I had a car once where I never resolved the problem. I rebuilt all four calipers and the MC, no difference. An out of alignment rotor can suck air into the calipers, I worked that path to death and found nothing. Searched for pinholes in the lines, nothing. Good luck, I hope it was just a poor bleed in the past.

 

Check the RAVE for the bleed sequence. It's not the normal "start with the furthest away and work your way to the master".

 

What does the fluid look like?

 

For air to get in the brake lines besides the obvious not-tight fittings, the fluid must be displaced somewhere else; either leak or calipers volume expansion.
The master cylinder reservoir had to go empty at a certain moment to suck air.

 

Fluid looks good. I think there is is a leak between the reservoir and the cylinder, so I'll just replace the entire assembly.

 

Check the wheel bearings for play.

Movement can move the pads apart, as the rotor moves sideto side, then it takes a pump or two to get them closer to the disc, then the final press actually acuates the brakes.