Is that 880 kilometer drive possible (for one day) and how
long would that take? (We're looking to take the A1 road, I trust that is an autobahn) ..

I'm looking at 1035 km (of which 89km/3h by ferry Gothenburg-Frederikshavn)
which Shell's GeoStar website claim (at moderate speed) to take 12h44min
and that looks quite reasonable to me...

Regarding the Autobahn, many stretches are posted 130km/h (don't know
the status of involved portions) and if you end up in a queue you can
lose a lot of time. IIRC, the major queue season hasn't started yet, but
getting around Hamburg can be a pain anyday - got stuck for three
hours/20km when on the way to the world exhibition in Hannover last year...

As to the Swedish part of your journey, most of the way is 110km/h,
some is 90 km/h. The fast lane usually moves 15-25km/h faster than
posted (busted for 30+ above and you lose your license for a while here).
If the traffic is reasonably dense and you follow the flow you're
generally ignored by the police - while keeping the same speed in
light traffic they probably would stop you.

Max speeding fine is IIRC 2000SEK (just short of US$200) but they
might also hold on to your lioense - as some the participants
(won't write what I really would like to call'em) in the Gumball Rally
a couple of weeks ago.

/Michael