As a senior citizen I am quite happy with the fellowship at my parish church. I would think that if I were a young adult there is room for improvement.
I am fortunate enough to make it to weekday Mass, which is held in the smaller chapel. After that we leave and have our conversations after we exit. In that way we get to know who is ill or had surgery recently. From that information the person can get visits and phone calls, and find out if any more help is needed. Some of us attend a breakfast at Denny's on Wednesday's after Mass, which we call "the breakfast of Holy Obligation".
Anywhere from four to ten people attend that at one time.
Once a month there is donuts and coffee/tea after Mass. We are exhorted to introduce ourselves to others and get to know them, where they are from, share what ministries we take part in, etc. What can start out being superficial, can end up in being a lifelong friendship.
On First Fridays we have adoration of the Blessed Sacrament starting after Mass and ending at 4:00 PM that afternoon. A shared breakfast is attended by most after that Mass, and knowing these people for quite some time the conversation is enjoyable.
On Friday mornings after Mass we meet once a week in the education building for "Reflection Time." We recently watched, once a week, the ten one-hour DVDs of Father Robert Barron called "Catholicism". They were very well received!
Now we are reading the book "Living the Mysteries - A Guide for Unfinished Christians" by Scott Hahn and Mike Aquilina. It makes for a lot of conversation of a spiritual nature. A lot of humor goes on with us senior citizens as we laugh away our aches and pains!
Of course we can't have fellowship with every member of our parish, but it is certainly possible to form caring friendships this way.
My parish is not strong on Bible studies, so twice a year I attend two other Catholic parishes that are presenting the Jeff Cavins Bible studies, and the EPIC one as well. (Church History). Some are once a week for 20 week, 24 weeks, or 10 weeks, depending on the subject.
We have one vigil Mass on Saturday, and two Masses on Sunday.
There are Scriptural Rosary gatherings in some homes as well, weekly and/or monthly.