I've used ~. for a long time but did not know about others. I know, should have read man page.
Anyway, if you try it from shell prompt it is likely will not work as pressing ENTER shows the next prompt. Try `cat` followed by ENTER and then ~?
No need – your local ssh client, which interprets the escape sequence, doesn't have any understanding of whatever mode the remote session might currently be in.
The point of the return is to prime it to accept the start of a new escape sequence. Presumably the idea is that `~.` is not completely unlikely to occur as part of text entered remotely, but less so at the beginning of a new line.
Same with me, I'll still instinctively go for ~. when a connection has hung / dropped (usually because of a NAT via a rebooted firewall), but never even considered how ~ doesn't normally cause an issue. Never knew it had to be immediately following a newline. Also never knew about the other options, ~^Z in particular looks useful.
I wonder if anyone still remembers the ctrl-[ sequence in telnet. I think I only ever used the quit command in that though.
It'll still work. OpenSSH doesn't care about output (for ~ stuff), only input, so if you type <enter>~. it will close the connection.