Brake booster?? catching, studdering, hard peddle

Ok 1998 lesabre 3800? cant go check and i keep forgeting which one. has bout 132,000 miles on it. For some time many months at least, the brakes would grab only sometimes and right at the end of the stop. They also would, i'll say studder right at the end. not like rapid anti lock but just bump bump real quick or maybe three times. this happens frequently now and the grabbing still happens but not so much. Not sure how long after the brake job year maybe I took it back and he found nothing.

Just yesterday we got the tires rotatated and they checked the pads and said they were fine. Assumeing they looked and well then pad is high and wearing normal. but after the rotaion the peddle was hard. i tested and it stops normal i think but the peddle feels harder. The brake fluid was down about half between max and min. Checked that at least on last oil change and was not like that. put some fluid in I missed that max mark but would think it close enough to improve if not fix, if this was the cause.

So I have not worked on brakes for many years and even then was minimal. just as cheap to have them done. So anyway what do i look for. It sounds like the booster is possible but I think not. How do you test or decide it is the booster, or anything else. If it is the booster I would like to replace it myself assuming it would cost much to have it done and assuming there is not much reason to have it done. as in difficult or risky.