AFAIK it just does NTP lookups. I don't know how often it's supposed to do that, IIRC there's a registry setting to set the poll interval. The time server used may impact functionality, e.g., the default MS time server may be timing out; you can try a NIST server.

Moving between time zones, don't know, hit or miss depending on various settings. Also, IIRC, it depends on your IP address, which is not always a good indicator of geography. Location services would need to be on as well (I think).

Updates may affect your settings, e.g., occasionally I've found my "update automatically" or whatever it is reset. I've never had to start the time service myself, but some people have, so that's something else to check.