[hwh]

No, it wouldn't. Your examples are mostly hints that it's actually your terminal emulator (which might also serve as your "SSH program" in cases like PuTTY) which might need a slap to behave correctly - and then your TERM environment variable and possibly LANG (UTF-8 support) should be set up correctly. tmux will work then.

[VikingCoder]

A util like I propose would be able to 1) ask what term / ssh you're using, 2) ask you to demonstrate keystrokes and mice and determine if they're working, 3) offer suggestions for how to fix them.