Hey guys. I'm having an issue and wanted to know what would be a good first step.

When driving and hitting the brakes about 50-60 percent, my brakes hold and don't give out but it sounds like the pump is hurting. It makes this bad noise and this noise continues for the rest of the drive.

A very similar noise occurs when i am driving and steer hard one direction or another. If i'm standing still this doesn't happen, and only happens when i'm going 15+ mph and turn the wheel at least 1 full turn one way or the other. Similar noise occurs, and continues for rest of the drive.

Are these the signs of the brake booster and power steering pump dying?

The car is a 96 328 with 137k miles. Thanks.

Another thing: When i'm standing still with the car on, if i hit my brakes about half way it sounds like i'm pushing air. Is there an air check valve on both sides of the car or just on the drivers side front? And is this normal or do i need to bleed my brakes?

Brakes and steering repairs can be handled by a lot of do-it-yourselfers, but it is definitely not for NEWBIES. It can hurt you , your family and other people bigtime. Thus, what follows are just my comments and are not intended for you to follow as directions for your repairs.
If you need to bleed your brakes, you will not hear anything, you will feel it like a mushy
pedal, or a sinking pedal after you have pressed it farthest down. Overall, you will have poor braking power. Bleeding is always recommended after 2 years whether your brakes are good or not.
Except for the pedals and vacuum assist(aka brake booster) making some kind of normal noise, the brake master cylinder or abs does not make any noise (except for the frantic pumping and release of the abs during a panic stop). When you hear air, while pushing the pedal, it is most probably the vacuum assist leaking vacuum, or in severe cases, the brake fluid leaking from the master cylinder into the vacuum assist plenum.
Check the hose going to the vac assist including the valve . If you are not having problems with your brake fluid level, it is needless to check for leaks into the vac assist. If the hose and fluid level are OK, then you may need a new vac assist.
Re- steering, check atf level and proper function of pulley belt, add atf if needed and bleed by turning strg wheel approx. 6 times with engine off. Check rubber boots of strg. gear for oil leaks or presence of oil inside. With everything normal, logic/price tells you that the pump should be replaced first before the gear box.