Cygwin Terminal and zsh strange characters used in username

It looks like zsh is inheriting the value of PS1 from the previous shell. The PS1 environment variable sets the shell prompt, and zsh used a different format for prompt substitutions than other shells. Try entering the following command after you start zsh:

PS1=$'%{\e]0;%d\a%}\n%F{green}%n@%m %F{yellow}%d%f\n%# '

If that works, add that line to your ~/.zshrc file.

That's also probably a good place to put your aliases.