You probably have your questions answered by now, but for what it's worth:

We got our Turkish visas ahead of time just to save the hassle. Also, in this case, we let the hotel provide transportation in for we arrived quite late. As I recall it was about $20 for the two of us but that was several years ago.

What to do in Istanbul? Just walk around and enjoy the atmosphere. Particularly if you are in the old city. There are ferries you can take, trams to ride, shops to explore and mosques to view. The tour will most likely take you to the biggies so enjoy just being there.

You will love Turkey - it is great! Jo in Sunnyvale