Yes, taxi is the way to go. The $7 fare is no problem to obtain as it is the official flat fare. The taxi booth at the exit will give you a ticket and will bring you to your taxi. It's up to you of course to choose a regular taxi (which will be perfectly fine) versus the nice hotel car. Personally, I don't se the interest for the $40 option, as we are talking about a 15 min trip.

Yes, there is an ATM at the airport, several in town. The closest to the hotel is further down the hotel street (Charles de Gaulle Bd, on the right leaving the hotel, on the other side of the street. 5 min walking from hotel).

I would say yes, but Cambodian cities are generally not so easy to jog around compared to western cities. Be careful with the traffic and don't forget it's very hot around there. Better to stay at the gym IMO.

I used their services (driver + guide) the 1st time I stayed there and was happy with the service. Of course, the hotel charges more than what you would find elsewhere. Alternatively, take a guide and just use a tuk-tuk. There are plenty everywhere and it will be much cheaper.

I don't remember spirits/wine at the REP shops, but that doesn't mean there's none. They mostly have local stuff (Artisan d'Angkor shop, etc). I never really paid attention to spirits. I'm sure there's some in PNH but REP ?

Enjoy this wonderful place and hotel . I'm jealous but will go back soon