I've been using SE for years now (specifically mostly Aviation SE) and still have no idea how to "invite someone to chat".
(Edit: if it matters-- and I'm now realizing that it might-- these questions are really specifically for Aviation Stack Exchange, and any other SE communities where the chat functionality is the same as in ASE.) More general answers are welcome of course, as long as they also address the specific way the chat features function in ASE and other similar communities.
The chat FAQ says:
To get another user's attention, mention them – type @ and then the first part of their name. Your mention will be highlighted on their screen – @someone. This will happen even if they are in a different room. Note that you can only mention @someone who has been in the room at some point. If you need to invite someone to your room, do it from the user's chat profile page or from the user card that pops up when you click on their avatar in a chat room.
What is a "chat profile page"? How do I find it? Do I have one? Could someone use it to invite me to chat?
Regarding: "or from the user card that pops up when you click on their avatar in a chat room", 99.9% of the time, the person I am wishing to invite to chat is not currently showing an avatar in a chat room. But even if they are, I don't see any button on the "user card" that says "invite this person to chat". Specifically, I want to invite them to an existing room, not to create a new room with that person.
Is the thing that pops up when I click on an avatar in a chat room called a "chat profile page"? Or is it called a "user card"? And whichever it is called, how do I see the other thing? The FAQ implies there are two different things. Is this correct, or are they actually the same thing?
Is the FAQ misleading, or am I just missing some things here?
Also, in the case where the person has been in the chat room before and has left a chat message, then if I "reply" to his/her message, does he/she get a notification in his/her inbox even if he/she is not currently in any chat room?
What if s/he's never been in the chat room and is not currently in any chat room, does s/he get a notification if I leave a message starting with "@(username) in the chat room? I'm assuming not...
So basically this question is both 1) asking for some practical help and 2) asking whether some content in the chat FAQ might be misleading.
PS: I reviewed this answer, but this feature seems to no longer be available. (Edit-- the reason for this has now been discovered, see my answer.)