Depending on the university, fraternity life differs.
At the smaller university my father attended, the fraternities were simply social with no residential accommodations with guys living in the dorms on campus. My understanding is that although there was a 'frat house,' its main functions were for dinner and recreation - billiards, darts, ping pong, cards, yard for football or volleyball, etc. There was a monthly social fee.
At the Big Ten university I attended, the Greek Life was somewhat different. Most members lived in the house. Typically, the guys had rooms, mostly with a roommate or two. Most frats had a reputation as being either a jock frat, party frat, or academic frat. Each frat usually had teams in all of the intramural rec sports leagues (flag football, basketball, softball, soccer, volleyball, swimming, team handball, etc.) that also included teams form the dorms and off campus residences such as an apartment complex. Most fraternities also participated in various philanthropic causes, often having a causes specific to their chapter, but also participating in campus-events such as a blood drive or a dance marathon supporting to local food pantry. Fraternity membership did include fees.
Alumni were able to choose to remain involved in some activities. For example, there were usually alumni events during Homecoming. A friend remains active with his frat by serving on the housing committee which oversees the real estate's upkeep (plumbing, HVAC, roofing, etc) and solicits funds from other alums when major repairs are needed. The alumni also frequently have a scholarship fund they support and many often serve a mentors to current members as they are making post-college career choices.