I am using my mobile phone as a hotspot for internet, to which I connect my laptop and desktop. As you can understand, I have limited mobile data I can use per month, so I am wondering if 3 systems that are running syncthing and are part of the same network use the local wifi without needing to send the data through the internet
They should, but you might have to explicitly configure addresses of each device, on all other ones, to make sure it doesn’t accidentally go out to the internet.
You could also set very low rate limits, which by default only apply to non-local connections to prevent it from eating all of your bandwidth.
Yes. Syncthing should do this straight out of the box. Verify that the “Address” for each remote device is a local address. If not, there are probably firewalls on the involved hosts preventing direct connections.