This means also that if I want all events generated since the server started, I should make an API call as soon as the server starts.
For example calling /rest/events?events=ClusterConfigReceived would create a subscription for events of type ClusterConfigReceived. After the first call, another identical call would retrieve all the events since the first call, because since=0 is the default. Correct?
Is the same subscription matched irrespective of the ip address sending the API call?
How can I just create the subscription without waiting for 60 seconds?
Does /rest/events (without parameters) generate a subscription for every possibile event type, or only the event types that already happened, or a single type-less subscription that is accessible only with that identical API call?
The IP address does not matter, no. The rest of your questions are answered quite well, I think, by the few paragraphs on the documentation page I already linked to: GET /rest/events — Syncthing documentation