- I do not personally have experience with this website
- Connecting to an SSH server with an SSH client is much like connecting to a webserver with a webbrowser. It is theoretically possible for bad things to happen, but automatic ("zero click") attacks of any kind are difficult to pull off when the software is up to date. Most bad things that happen come from the user doing it themselves, like downloading and running untrusted programs, entering your password on a phishing site, etc.
- This is not necessary, given your host system is up to date.
Note that my answer to 2 is heavily oversimplified, but applies in this scenario of SSH to "OverTheWire".