Should I get my brakes checked?

My parents own a 2009 Ford Focus that I've been starting to use most of the time now to drive to school. Last week, I just got an oil change done and had loose links replaced for the front sway bar. Tire rotations and fluid top offs were included as well. I realized a few days later that the brakes were stuttery or jumpy (I didn't feel it in the brakes, but when I used the brakes more gently, I could feel the car kind of pulse to a stop instead of smoothly glide to a stop). A few times, a warning flashed quickly that the brake fluid was low for a split second and then turned off. My dad topped off the brake fluid and said not to worry because the brakes were replaced last year. I don't know if I trust what he says because he also takes his other cars for oil changes when they're way overdue and says they're fine. If I continue to have these problems, my dad will probably say I'm overreacting and he won't want me to take the car back in. What should I do?

Added (1). The car's steering wheel also vibrates at a stop

Nope

I'd have the brakes checked by a professional. Some places will do this for free while others charge a service charge.

If the brakes were replaced last year, your overeacting. But, if they weren't like you suspect, go have them checked. Most service places will check them for you for free, and they should, and might have been checked by your latest service job. Now, the pulsating in the pedal when lightly pressed, is normal. That's just the way ABs braske systems work, and that's what type a system is on your vehicle. Instead of the old days, where foot pressure dictated brakeing, they now pulsate, like you observed, that prevents locking up of the brakes on wet, or slick surfaces. Ice, snow etc etc. Keeps you from slidding, well, its suppose to anyways. If it makes you feel better, go have them checked. Your doin great in my opinion.keep it up!