To check for a dragging brake, simply jack up the car and in neutral spin the tires and see if there is excessive drag. A sticking caliper or warped rotor will be pretty obvious.
As far as engine hesitation, a lot of times a car just needs a tuneup-air filter, cleaning the throttle body and maybe plugs, wires and fuel filter etc. What's the status on that? But also check condition of vaccuum hoses and for vacuum leaks and check fuel pressure is at spec. One thing that can often cause some hesistation is dirty injectors. A big bottle of Techron fuel cleaner that treats 20 gals can help.
Another thing that can cause a hesitation feel is the transmission fluid and filter overdue for a change. Ideally you'd want to change the filter and flush all the fluid out through the cooler return line and replace it with Dexron VI. But at least drain and change the filter and refill with Dex VI.