Car is hard to start and when starts chugs and brake becomes hard to push

code p 0720 refers to output shaft speed sensor (OSS)---circuit malfunction===causes ---wiring --- OSS sensor--- ECM---TCM
as the OSS reports shaft speeds to the TCM so that he correct ratio can be selected, I would be having it tested / replaced

_______power brake booster, check vacuum to booster and the check valve for brake booster. primary symtom is high hard pedal that requires greater then normal pedal pressure to stop car. testing booster= pump brakes several times with engine off to deplete stored vacuum. turn on engine with pushing slightly on brake pedal. you should be able to feel the pedal fade away a bit, and then become firm. But not hard. if you feel nothing at the pedal when engine starts. Brake booster is not working. Good-day! make sure vacuum is going to booster with engine running. it may just be a bad vacuum line or check valve.

Hard start, no start, chugging acceleration, synthesized RPM limiter, sputtering idle.
Just to name a few.
MAF sensors can also become dirty. They are essentially just a piece of wire, dangling in your intake tubing. Over years they can become filthy. Auto part stores sell a brand of cleaner called Mass Air Sensor Cleaner, brand name is CRC. It's good stuff. Just take your MAF off the car, and spray the little sensor wire down with it.
If you are able to see the sensor wire, it should be pristinely white. As white as the background of this page. If it is not, clean it.

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tune-up, dirty gas, dirty air filter...when last completed?

Fuel or spark issues can cause this . Transmission lockup clutch can make a chugging sensation . When in overdrive lightly touch the brake while keeping a steady throttle and see if the chugging stops . Post back .

check the fuel filter and pump sounds like dirty fuel

the booster is the problem, or a hole or leak in vacuum line to booster check the check valve also ! from manifold. heres the symtoms of a bad brake booster. primary symtom is a hard pedal on application, to test booster. pump brakes several times with engine off. to deplete stored vacuum. turn on engine with pushing slightly on brake pedal. you should feel the pedal fade away abit and then become firm. but not hard. if you feel nothing at pedal when engine starts, brake booster is not working! check the vacuum lines first!!

well, a hard firm pedal, usually indicates a bad brake booster or a vacuum leak to booster or the vacuum check valve, on booster. TO TEST BRAKE BOOSTER; pump brakes several times with engine off to deplete stored vacuum. turn on engine with pushing slightly on pedal. you should feel the pedal fade away a bit and then become firm, but not hard. if you feel nothing at the pedal when engine starts the booster is at fault. good-luck !!

Is there a service engine soon light on related to this engine behavior?

Take a look at the fuel pump which is located in the fuel tank under the back seat.

Good luck.