For relationships, I figure the dwarfs "interact" by proximity. I know that a sparsely populated fortress generates less friendships, marriages, and babies than a dense fortress, all without any meeting areas of any kind.
I don't know if dwarfs interact when passing each other during a job. But, between jobs they'll mill around, and there's a higher chance of two dwarfs being near each other in dense fortresses. Meeting areas accelerate this. This would also be why soldier dwarfs make friends, but usually only with other soldier dwarfs at first. They spend a lot of time in the barracks together.
I also thought that dwarfs with a room may sleep somewhere else if that room's beds are all occupied. One thing that I haven't figured out is if dwarfs will use the unassigned beds in a room, even if they are owners/co-owners. At least, with some creative constructing, it's possible to create a single room with two non-overlapping room designations from separate beds, then give both beds to the married dwarfs.
If you do the one-tile meeting area, make in in a closed room at the bottom of a really tall shaft. Drop animals down there and your dwarves should start to get used to death and possibly prevent tantrum spirals. Also do it as an experiment to see if dwarves with the "doesn't care about anything anymore" trait will form relationships.
Regarding this, is there any way to reliably get animals to stand on top of a floor hatch or bridge? My livestock always follows their owners or assembles in the meeting halls unless I chain them up. And sadly, animals with owners can't be chained.
You can trap owned animals using some tricks, but it's easier to just take strays and pit them.