A day includes all trains that (are scheduled to) depart between 00.01 and 23.59 on the given date. As long as you board the final train before midnight it can travel into the next day without you needing to use a second pass day.

Once you leave a train past midnight you cannot board a further train without activating the next day in your pass.

For the travel between Lyon and Copenhagen you need 2 travel days. Then another travel day from Copenhagen to Oslo. The travel between Oslo and Bodo is 1 or 2 travel days depending on what departure from Oslo you choose. If you take the night train from Oslo to Trondheim and the day train from Trondheim to Bodo it will be 2 travel days. If you take the day train to Trondheim and then the night train to Bodo it will be 1 travel day.

It might be wise to check the availability on the trains and make reservations before you buy the pass.

In SUMMER-and with a lot of luck, you could, perhaps, make the trip from LYon (does not matter Perrache or PartDieu) to Cph-via Strasbourg-Mannheim-Hamburg and the overnite seats only from Hamb to Cph in 1 travelday. I wish you luck with this, as very often ICE trains in DE on DB are very, very late.

As explained above: it does not work in segments of 24 hrs-as is also very clearly explained in the general info, but in calenderdays, so if you start at exactly 0.01 you get indeed 24 hrs.

Extra: actually now that the new SJ/SE overnight train from Hamb also runs all year-you could even reach Stockholm in 1 travelday-same forewarning as above.

IMHO - go for the 5 day pass for an extra 25 euro or so.

The 4 day option involves a lot of if’s and either overnight seats or fees for beds.