Your questions 1 to 5 are all about praying with people of other faiths. Jehovah’s Witnesses would not distinguish between Mormons, Catholics, Jews, or Muslims here: all are equally “other faiths”. As such, these all collapse to one question*: Do Jehovah’s Witnesses pray with non-Witnesses? The answer is No, they don’t.
Praying with members of other religions is practising a form of interfaith, which the Witnesses strongly condemn:
A clearer deliniation of what does and what does not count as interfaith activity from a Witness perspective is in the article “Would it be a form of interfaith to purchase a building from another religious group and convert it into a Kingdom Hall?” in The Watchtower, October 15th, 2002. While the article is specifically about the situation described in the title, the content does actually clarify their definition of interfaith activity better than anything else I can find from them. (There is no article on Interfaith in the Insight book, for example.)
Certainly, prayer with another religious group would count as interfaith activity, and would therefore be condemned. See also, Why do Jehovah's Witnesses not pray with people of other faith?
* There is one possible exception:
Would prayer be an option (or recommended) when meeting a Mormon in his home to teach him?
It’s the last few words which give this one a slightly different flavour. Witnesses spread their message to strangers, both on the streets and by working from door-to-door (and in sundry other ways from time to time, but those are the main two). This is initial contact. However, once someone has expressed interest, Witnesses will probably call back. If someone wants to learn, they will establish a “Bible study”. This is a semi-formal arrangement, in which the Witness will regularly (weekly, perhaps, or whatever suits everyone’s schedules) call back to the person and work through some material explaining Witness doctrine.
In the eyes of the Witnesses, at least, this is a one-on-one educational programme. (Well, usually. Sometimes a couple or even a whole family will study together. Often, the Witness will bring another Witness along, but that might be a different person each time, while there’ll be one regular conductor of the study.)
The “interested person” may or may not see themselves in the role of a student. They might see themselves as an opponent in a debate, or merely someone interested in discussing alternative worldviews. Whatever.
Once such a study has progressed a certain amount, the Witness is likely to open it by praying aloud. So once a regular educational arrangement is set up, yes, a Witness would pray in this situation. At this point, though, they’re seeing the person as a prospective convert, not a firm Mormon, so they wouldn’t see it as praying with a Mormon. Furthermore, it’s unlikely they’d be comfortable with the other person leading such prayers, though doubtless they’d encourage them to pray privately (and with their minor children).
That was a long footnote, but I have one further elaboration. There’s a difference, a big difference, between praying with someone and praying for someone. If someone asks a Witness to pray for them, they probably will, maybe even aloud and right there and then. I have heard of Witnesses doing their general door-to-door work, and having the door opened by a distressed person who saw someone religious and asked immediately for a prayer. In that situation, the Witness will probably pray. And if the other person joins in (who knows how a stranger will react? and people praying aloud together, talking over each other, is the norm in some religions, so the person might do that), then that means that, technically, the Witness is praying with someone of another faith.
I don’t know exactly what the theological reasoning is which says that this is acceptable. I do know that I’ve seen anecdotes including such spontaneous prayer on demand described approvingly in Witness publications. If someone asks a Witness to pray, in a private situation, they’ll pray.
- Organised interfaith event: No.
- Bible study with someone who’s not a Witness but may be heading that way: Yes, with caveats (the Witness would offer the prayer, generally speaking).
- When asked by someone who seems distressed: Sort of (this is praying for, not praying with, but if the other person joined in and converted it into praying with, then the Witness is unlikely to complain (especially if the person is distressed)).