There is one genuinely useful thing to know: a Skånetrafiken ticket bought all the way to a Danish station is a real through-ticket. Buy Lund C → København H in the Skånetrafiken app and you are covered for the whole trip, bridge included, and you do not need anything Danish. Öresundståg and DSB sell the same crossing from their own sides.
Since December 2024 an Öresund single is valid for a block of time rather than for one journey — 2, 3, 4 or 5 hours depending on distance — with unlimited travel inside that window and no direction to declare. A 24-hour ticket costs about the same as two singles, so a day return is often the simpler buy.
The catch that catches everyone is the Copenhagen Metro. On a single or a 24-hour ticket the Metro is included. On a 30-day or Flex pass it is not: that needs a paid Metrotillägg on top. Skånetrafiken does not publish a fixed price list for Öresund singles — the app quotes the fare for your date, and any figure you find on a search engine is likely to be a 30-day pass price rather than a single.