I just came across this tool, which - after entering a city - shows all other cities to which there is a direct train connection. A color code depicts the travel hours.
Although I'm not quite sure yet on what occasion I can use the tool. But someday the moment will come :D
Btw. there is a Sparpreis search on https://bahn.guru/ with a monthly view ("On which day do I travel cheapest from A to B?"). Unfortunately the links to the store don't work yet.
It wouldn't if you calculate it once globally and cache the result. It is not as if the results for the second hop change depending on where the first one came from. The travel times might be tricky though if you want to consider delays between hop 1 arrival and hop 2 departure.
direkt.bahn.guru internally uses a (legacy) API by Deutsche Bahn to find all direct trains running via a given station within the next 1-2 weeks. This API includes most trains in central Europe, but data availability gets significantly lower the further away stations are from routes (co-)operated by DB. Furthermore, trains operated by smaller companies seem to be missing more often than those run by state-owned operators, probably due to a lack of data sharing agreements.