TRAMP doesn't open any network connections at all. Instead it relies on ssh (or ftp if you're really old-school).
Open up your ~/.ssh/config file and set "ControlMaster yes", "ControlPersist yes" and "ControlPath ~/.ssh/cp-%C" and ssh will multiplex all of your ssh sessions across as few unique tcp connections as possible. This will speed up scp and sftp connections as well.
Same. One of my wishes for Emacs in "From caching up to getting ahead" is for Tramp improvements.
These days I went back to TUI Emacs via SSH for work.