For terminal, acme have support for windows attached to programs (if the program is a shell, you have something like a terminal). From the manpage:
Win creates a new acme window and runs a command (default /bin/rc) in it,
turning the window into something analogous to an rio(1) window.
Executing text in a win window with button 2 is similar to using Send.
Mail client is builtin but only for upas/fs. If you want/need another approach you can extend by external programs.Some other applications of plan9 have taken the advantage of acme UI (like abaco web browser) but they aren't builtin inside acme.