Deleted

Yes, if those processes are running in the background.

Of course, the Linux machine is doing the processing, so you can safely shut down your Mac and later reconnect to the same Linux session and check the process.

You want to use 'nohup' for any long process with a '&' at the end. For example: nohup wget http://really-big-file &

All output from that will be stored in nohup.out and you can check it later.

Forgot to close the thread?

You maybe want to get a terminal multiplexer like tmux or screen. It gives you multiple terminals in one window, so you don't have to log in for every program you want to start. It also takes care off your processes, so they keep running when you exit the ssh connection.