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Is the mass the same as a Sunday mass..
Same basic format as Sunday mass, but read from a different part of the book.
What happens at the burial...
This is not part of the Mass and doesn't even necessarily need to coincide with the Mass for the Dead. It's pretty much the same as at any other secular(ish) event.
Where is the eulogy given...
A eulogy is not part of the Mass, the Mass is for the repose of the soul of the deceased, not to honor his or her life.
However, eulogies are often given, after the priest has spoken his homily (about halfway through mass)
Is it practical to skip the mass...
That's entirely cultural and subjective. The only thing a non-catholic shouldn't do at Mass is receive the Eucharist. Beyond that, do what is comfortable. Chances are very good that over half of the people with you are cultural Catholics and wouldn't give a hoot if you sat through the whole Mass.
One thing than is probably acceptable (at least in a traditional sense for those who are not fully accepted into the Catholic Church) would be to leave after the homily (or the eulogy). That way all you're hearing is the stuff you've probably heard before and all the stuff you're missing is the stuff you might feel uncomfortable either in participating in or visibly avoiding. So then you can mill around for half an hour or so and join the entourage to the cemetery when you see the casket being carried out of the church.
What are the cultural/social norms around interacting with the mourners?
It's always dependent on the circumstances, but generally Catholic funerals are pretty happy events, even if the death was fairly tragic. My brother, who died at 29, was an awful experience, but I got hugs from nearly everyone in the entire town and felt good to have the support of everyone who knew him
Are you supposed to bring a dish to the luncheon?
Probably not (unless it's a funeral of epic proportions) this is usually handled by the ladies of the Parish who seem to have the uncanny ability to materialize tons and tons of food out of nowhere.
more info on Funerals from the US Council of Catholic Bishops. Apparently, in extraordinary circumstances, non Catholic's can read at the Mass.