There could be several potential problems. Pertaining to the question on the park brake. Does the mechanism stay locked, but the brake still slips? Is there visable damage or wear on the drive belt? Regarding the drive belt system itself, likely failures would an idler (likely flat idler) that is damaged or quite possibly the drive pulley itself is cracking and separating.

Your tractor has a hydrostatic transmission. While the drive belt could be the cause of your problems, I tend to doubt. However, since it's relatively cheap, I'd change it first and then proceed to more complex repairs.

In all probability, the hydro is beginning to fail. Have you consistently kept the transmission cooling fan and fins clean of debris? Overheating is the kiss of death for small consumer hydros. Have you been towing or used any ground engaging attachments?

As for the brake, it is adjustable, even though the owners manual from Sears tells you to have it serviced. The brake is on the right side of the transaxle, just below the cooling fan. You can get access by jacking the tractor up, and removing the right side wheel. The brake consists of a small wheel or rotor mounted to a stub shaft. A moveable brake arm connected to pedal linkage cams against two pins which in turn push the brake pucks against the rotor.

To adjust, there is a castellated nut mounted on a stud of the brake housing. Remove the cotter pin and turn the nut clockwise to take up some of the slack. Dry fit the wheel and let it down to the ground to check braking action. Tractor should roll easily with no brake (and with freewheel or bypass disengaged), yet when brake is applied should cause wheels to lock up and skid. You may have to repeat several times to get it right. Then replace cotter pin on castellated nut and permanently fit the wheel with the appropriate washers and snap rings.

Make sure you're not too tight, causing brake to drag. This will cause premature wear, reduce power and performance to rear wheels, and create a possibly damaging load on the hydro.