How can I prepare for cycling 60 km, before getting the bike?
Edit: As discussed in the comments, I assume that OP is allowed to take a total of 2 hours of breaks, not that the ride (moving time) itself must be shorter than 2 hours. A 30km/h average speed over 60km would be challenging even for an experienced rider on good (but public) roads on a road bike.
It sounds like you are in quite a good shape. You should easily be able to do 60km in a day on a halfway decent bike. Unless there are lots of hills or headwind or bad roads. My sister recently got her first cheap 250€ city bike and imediately did a 90km trip along the Danube river without any issues. She didn’t do any bicycle specific training before but can probably perform all the exercises you mentioned.
Just take it easy, take a long break in the middle and remember to eat (but not too much and mostly carbohydrates, e.g. fruit or pasta or rice) and drink enough.
A wide saddle can chafe on the inside of your legs. A very soft saddle can put pressure on areas where you don’t want it. The specifics depend a lot on your body and your seating position. Just try the saddle which comes with the bike. Get bicycle shorts or at least tight shorts (e.g. running shorts) and wear them without underwear.
Adjust the saddle position to be high enough. As a rough estimate, with the pedal at the 6'o clock position and your heel placed on the pedal your leg should be fully extended. Considering your core strength you can probably lower the handlebars as low as possible for better aerodynamics.
You can’t really train endurance within 10 days. I’d take a few short rides (an hour or less) so your body gets used to the movement. Make sure your seating position is as good as possible and everything else is set up correctly (tire pressure, chain lube, shifting etc.) Don’t overdo it, you don’t want to start with sore muscles or a sore neck.