sorry cannot help, I have been there more than ten years ago (hmmm, rather fifteen years), not much to worry about security at that time although we just stayed for a few days
as for the engine yes you should really be ok, average current was 2/3 knots, but it gets much stronger in some places, usually where a millions ferries cross from one side to the other of the strait..
Never sailed there, but I took a look at the yachting facilities when we visited in 2002. The Atakoy Marina was modern, well-kept and had decent security, in a good area not far from the airport. It looked fine to me. The drawback is it is about 10km from the town center. But the main rail line passes close by, so maybe there are commuter trains. Not that cheap, I think I worked out my yacht would cost around 25€ per day.
Otherwise, the only other place with yachts I noticed were on moorings in an old, run down harbour on the south side of the old town. That did not look so good. There were none at all in the Bosphorus, which as I'm sure you know would be a real challenge for a yacht to pass through going north.
Atakoy was good/clean but expensive.
However neared the city, we saw many yachts etc on bouys all over the place.
We stopped a night in a little fishing port at the black sea end of the bosporous paid nothing, - and had no problems.
There are so many boats around - so there must be many places to pop into.
Current in the middle of the Bosporous was only 1 -2 knots
(I dont know about the Asia side - we never got over there)