Help with booking SJ346 Hamburg to Stocholm

My wife & I want to travel from Berlin to Stockholm overnight 5 October 2023.

I see that the train runs from Hamburg to Stockholm on this date so we will travel Berlin to Hamburg late in the day & connect with the SJ346 departing Hamburg at 21:19.

If we travel Berlin to Hamburg to Stockholm - that’s 2 train trips on the one day - does it count as only 1 Eurail pass trip for each of us?

I’m also confused about the types of sleeping compartments available, We are 1 x male & 1 x female; what type of compartment do we book?

Also there are ‘Seat in sleeper compartment (1660SEK) or ‘Own sleeper compartment’ (1654SEK). What is the difference? The later would be our preference.

All help/advice appreciated.

Thanks