*3 years in Ph.D. Don't attend drinking parties. Slightly introverted. Making friends slowly.
For cohort: It's not abnormal that cohorts get close. It depends on the department and the cohort dynamics. My cohort are considered the most collegiate among all 5 or 6 cohorts in my program by the end of our 1st year. We are closer in age, few married or with children, most living on campus, no one too invasive or dominant, no strongly exclusive cliques. There are some regular dining out, trivia nights, game nights in our first year, like weekly or biweekly, but nothing mandatory. I'd say let it be natural. Making friends is indeed only partially in your control. If you'd like to bond your cohort, go ahead but know that in grad school, people may be more independent or want closer/smaller friend network. Openness and understanding are the keys.
On campus: in my undergrad and current institutions, grad and undergrad are not closely connected. I do have undergrad RAs in my lab, but I don't bond with them due to power dynamics. I still go to events on campus, like performance and talks, recreational sports classes, etc.
About age: what is the "active ingredient" about age? Otherwise it's just a label.
Typical weekend night: one thing about grad school is to be comfortable with not being typical, especially in the domains you asked about. Follow your feelings and do what's comfortable for you.