There is not a specific ritual for approaching the casket, and the Church does not disdain the prayers of Jews or those of other faiths which are offered for her children, whether living or dead. Everyone is welcome to come to a Catholic funeral, even atheists. (Praying out loud in Hebrew in a Catholic church is not wrong, but it might freak someone out…probably not something you’d venture to do, anyway.)
If you happen to run into the family of the deceased or talk to a fellow mourner, you aren’t expected to “say” anything in particular, you may let the bereaved do the talking, and so on, and that is all appropriate. It is better to keep loud conversations outside the church, but this is often ignored, alas. Don’t follow the lead of others on that one…you won’t be thought “stuffy” if you keep your voice down while others get loud! Those attending the funeral often go ahead and offer their words of consolation before the burial, though, if they run into someone close to the deceased and they are so inclined. Still, if the funeral is at all large, it is not possible for everyone to talk to the family, very often the family waits in a separate place and only takes their seats immediately before Mass starts. Some of the Jewish customs about all the things you *don’t *do when around someone mourning someone close to them would probably be very good customs for Catholics to adopt, though!
There is certainly nothing that says you have to approach anyone before Mass, for instance, although it would be good to acknowledge someone you know if they are standing around alone and not occupied with someone else. Otherwise, you may simply take any program that is being offered, sign the guest book if there is one there (so the family knows you were there, as they can’t remember even who they talked to directly very well), and take a seat. The reserved seats are clearly marked and all the others are open on a “first-come, first-served” basis, so to speak. If in doubt–that is, if you don’t see that anything is reserved–go ahead and leave the first five rows or so open. I don’t think you can go wrong with that.
The casket is sometimes open right before Mass starts, but it is very rare for the casket to be left open in a place where the mourners cannot avoid viewing the body, and there is a reason for that. It is not rude to refrain from viewing the body. It is not rude to refrain from going to the interment after the funeral Mass, either. It is not rude to refrain from offering Christian prayers or to refrain from reciting Christian creed, nor to refrain from making the sign of the cross or genuflecting before you take your seat. (Well, Catholics ought to do it, but it is understood that people who do not believe in the True Presence will usually not.) It is also not rude to do these things if you are not Catholic; the only thing you may not do is to receive Holy Communion. You usually will stand when everyone else does, but it is not rude for a non-Catholic to remain seated while others kneel. Usually the priest will explain these things, but if he’s been told everyone attending will be Catholics accustomed to funerals, he might not. There is not a custom among Catholics that the body of the deceased may not be left unattended.
It is not uncommon for the homily (the talk after the Bible readings) to not be all that specifically about the deceased. The homily is not the eulogy. There does not even have to be a eulogy at a funeral Mass. If there is a eulogy or eulogies, that/those will be done after communion. (If it is a Mass; there is a ritual for a funeral in the church but not a Mass, which the family may opt for if most of the mourners will not be Catholic.) Sometimes there is an open microphone offered at the time of the eulogy for those who want to say a few words, but no one in particular has to say anything. Still, no one is prohibited from doing so because they are not Catholic. (I mean that during the eulogies, if those present are invited to say something if they like, the guy in the yarmulke is allowed to speak in a Catholic church.) It is good to keep such remarks very short unless you’ve been asked by the family to say a few words, though. If someone says something funny, it is OK to laugh during Mass. The Mass is not officially over, though, until the priest or deacon says, “The Mass is ended, go in peace.”
There is sometimes a funeral luncheon after the funeral Mass and before the interment. It is not out of place to exchange fond memories of the deceased, or even to simply have pleasant conversations with whomever you see. Sometimes weddings and funerals are the only places that extended families ever seem to see each other, so there may be a lot of levity at a funeral luncheon! You can never tell; just follow whatever the mood of the group seems to be. It is common in some places for the funeral luncheon to be the place where everyone tells their funny or fond stories about the deceased, to “celebrate” the life of the deceased. It is sometimes a good deal less somber over at the parish hall than you might think, and this is considered a good thing. Keep an eye on what the family is doing, but usually laughing is OK and usually at least one of them will be doing it, in order to give permission for it to everyone else.
