Transfer service: I just returned from Turkey and used Welcome Pickups for my airport ride IST-Sultanahmet. Traffic in Istanbul can be a nightmare - whether you take bus, taxi, or shuttle service you'll have the same issue. Welcome Pickups is flat fee no matter long it takes but a taxi runs on meter. I didn't bother with the metro due to the multiple changes required to get where I wanted to go. My driver was very communicative through their app and also WhatsApp, he even sent a video showing precise instructions to get to the meeting place. They monitor your incoming flight and will know if you're late and will wait an hour after your scheduled pick up time. You can also message the driver directly if your flight is delayed. The Istanbul airport is HUGE and it takes a good while to get from your plane to passport control. Based on my messaging with the driver, I got off the plane with my carry on luggage, went through passport control, and was at the meeting point 22 minutes later. It took about an hour to get to my hotel during moderate traffic. My driver commented that the Sultanahmet traffic was less than he expected. I used the service for a return shuttle from Kusadasi to Izmir airport and had a fine experience, though the driver was not as communicative and was five minutes late to pick up, but we got where we needed to be.
Food tour: I did a Foodie Tour in conjunction with a Rick Steves tour, operated by SRM Travel, the company that provides all of RS guides for Turkey. It was fantastic. We spent the entire time on the Asian side and not only did food things but learned a lot about how real Istanbul residents live outside the tourist center. We sampled about 20 different foods and it was a splendid (and filling) day out. SRM may be able to offer a private tour or possibly fold you in to an already planned tour if you contact them directly.
Ferry: I can only speak for the short Bosphorus cruise we did on the RS tour - we took a private boat which ran about 1.5 hours and turned around about at the Rumeli Fortress (we were dropped off on the Asia side to meet our tour bus). It was a fine experience to see the city from the water, but with your limited time I would honestly spend your time seeing other things.
Restaurants: I didn't eat at any seafood restaurants, but our guide pointed to Akın Balık Karaköy as one dinner option for fresh fish. YMMV.