1) Every guest is entitled to be invited by name, with an invitation sent to their own home address. If they are permanent co-habiting members of a committed relationship, then they can be named on the same invitation; otherwise they should each be sent their own invitation.
Traditionally — by which I mean, the accepted practice over the last two or three hundred years; not a website that’s been up long enough to be indexed by Google — two cisgendered opposite-gender people living in a committed longterm coital relationship were always presumed to be married. Two co-habited people of the same gender, or of ambiguous gender, or more than two people, were always assumed to be living in a fraternal relationship. Too prurient an interest in the legalities of a couple’s wedding contract, or the bed-sharing habits of a private household, was considered vulgar. I still consider prurience vulgar. A married couple is addresssed as:
On an outer envelope in the U.S.A. or on a business document: Mr. and Mrs. John Smith (if they both go by the husband’s name) and Mr and Mrs Smith on all other formal notes, labels, invitations, and inner envelopes. In the English-speaking world outside of the U.S.A., outer envelopes are addressed only to the female head-of-house: in this case it would be addressed to Mrs John Smith.
On an outer envelope in the U.S.A. or on a business document: Mr. John Smith and Ms. Jane Smith (if they each go by their own name — even if the they have taken the same surname but use different given names) and Mr and Ms Smith on all other formal notes, labels, invitations, and inner envelopes. A lady also has the option of using “Mrs Jane Smith” or, if she has kept her father’s name, she may choose to use “Miss Jane Doe“. SHE gets to decide which she uses, regardless of any political opinions you may have on feminism and name expression. If you don’t know your guests’ preference, you need to ask. A same-sex couple is addressed on outer envelopes as Mr. John Smith and Mr. Thomas Smith or possibly Ms. Amelia Andrews and Miss Barbera Baker following exactly the same logic as for an opposite-sex couple, and as Messrs Smith or as Ms Andrews and Miss Baker on all other formal notes, labels, invitations, and inner envelopes.
A single person, of course, is addressed as Mr/Mrs/Ms/Miss Kelly Smith on outer envelopes and as Mr/Mrs/Ms/Miss Smith on all other formal notes, labels, invitations, and inner envelopes. As above, you have to figure out what title they prefer.
2) If people are married (or presumed to be married, see above) or are engaged (or have been a couple long enough and exclusively enough that they should be presumed to be engaged) then both members of the relationsip should be invited. Even if they are engaged, if they are not cohabiting then they need separate invitations. If you want someone who is single to have a companion at the wedding, then you call or write them a note asking “is there anyone you would like me to invite on your behalf?” They provide their friend’s name and address, and you invite their friend as a full first-class guest in his or her own right.
3) If you actually follow traditional formal etiquette and invite all single people by name with their own invitation, the you can pick or choose all you like as long as married and engaged couples (as described above) are invited as a couple. No-one will know that you invited Cousin Phoebe’s boyfriend as her plus-one but didn’t give a plus-one to Cousin Lysander, because Cousin Phoebe’s boyfriend got his very own invitation just as if you actually knew him. As hostess, it is not only your right to be selective about the guest list, but it’s your obligation. Everybody in the family knows that Lysander’s boyfriends are always jerks, and you shouldn’t be imposing his latest fling on the rest of your guests.
4) The rule is, that married couples’ names go together on the same line joined by the word “and”, and unmarried guests are listed on separate lines without the word “and”. They still all get their names used, though. So, two sisters living together in a long-term committed household (or two in-the-closet lesbian roommates) are invited as:
Miss Sophia Phipps
Miss Arianna Phipps
on the outer envelope and as
on all other formal notes, labels, invitations, and inner envelopes. Neither Sophia nor Arianna gets to be addressed as “Miss Phipps” on these correspondence because that title belongs to the eldest unmarried Phipps lady and their Grand-aunty Aspasia holds the title.
In the eighties, prurient etiquette mavens latched onto this separate-lines-and-no-conjunction rule to address co-habiting conjugal couples who didn’t have a marriage certificate, as a way of subtly rubbing in that their household was second-class and disreputable. I consider that practice horrid. But it IS appropriate for addressing siblings or children. For a couple with children, you would combine the two forms:
Mr Daedalus Jones and Ms Persephone Smith
Children should be named ONLY on the inner envelope or on the write-in line of the invitation; never on the outer envelope. Since a write-in line is often narrow, children can be written in on the same line squeezed in under their parents name, separated by commas or extra space and without the conjunction “and”.
5) I despise RSVP cards and refuse to use them, being one of the last holdouts of traditional etiquette that considers them to be in poor taste. This is just one more reason to dislike them. My understanding based on twenty-seven grand-nieces and grand-nephews is that up until about three months, babies don’t sit on their own and are in a sling or a carrier. They don’t need a seat. Up until about two they need a high-chair and until about four they need a booster seat. Sizes and back-strength vary so those are general break-points. Provide a chair for everyone age two and above and include their chair in your count. For people between four months and age two, do not include them in the count but arrange to have a high chair, and hand-write in beautiful script: “In addition _____ high-chairs will be provided.”