

I’d check https://transparencyreport.google.com/safe-browsing/search because most browsers including mozilla firefox rely on google safe browsing.
The other thing to point out is that if an attacker somehow got root access, they could install a so called “rootkit” and what it does it replacing some of the basic commands like top, ps, … with altered ones in order to hide the malware activities
yes Syncthing should work just fine just make sure to only sync the save directory to minimize bandwidth. rsync is another common tool (at least for Linux) that does same job through command line. making it easier to automate the syncing tasks through bash scripts