Send a command to a running tmux session (like screen -X)

I think this is close to what you want:

bind-key X confirm-before -p "Kill #S (y/n)?" "run-shell 'tmux switch-client -n \\\; kill-session -t \"#S\"'"

Your #3 approach is along the right lines, but the problem is that confirm-before does not do status-left-style substitutions (e.g. #S) in its command string.

A caveat for the above binding is that since everything is done in from run-shell, the commands are run outside the context of any particular client or session. It really only works because the “default” client (for switch-client) and “default” session (for #S) are the most recently active ones. This works out as you would expect as long as you only have a single active client (e.g. a single user that does not type into another tmux client until after the shell commands have finished running); it could fail dramatically if (e.g.) you trigger the binding in tmux client A, but new input is received by tmux client B before the shell started by run-shell has had a chance to run its commands.

This particular race condition seems like a nice motivation for providing client/session/window/pane information to run-shell commands. There is a TODO entry about getting if-shell and run-shell to support (optional?) status_replace() (i.e. status-left-style substitutions), though maybe a better choice would be format_expand(), which is kind of a newer super-set of status_replace (offers #{client_tty}, etc.).

You can attach to a running tmux session and spawn a new window which runs a particular command:

tmux attach \; new-window vim

Note that this does not spawn vim in the pre-exsiting window - there is no facility for doing that, it doesn't really make sense: as @Falcon Momot points out, an existing window could be running anything, the only way to issue commands is "send keys".