Here are a few other usage examples. 1) I've been a commuter my whole career. Sometimes I've commuted by car and sometimes by train. 2) I used to commute forty miles each way by car. 3) It was a tough commute. Route 128 was congested. 4) I live near a commuter rail station. When I worked in the city, I was able to commute by train, so at least I could read during the commute. 5) The Massachusetts Bay Commuter Rail service, MBCR, seems less reliable since Keolis took it over.

Yes. In fact, I used to commute by train every day.

Yes - both sentences are good and normal English.