I am only replying because I found your comment about drivers interesting: generally AMD is known for having immature drivers and Nvidia for being quick with the fixes.
Anyway, although I have no experience with these cards, I can tell you:
1. On it? No, not without some modification to the cable so that it could connect to the motherboard. However, they can be controlled by some GPU software, like MSI Afterburner, which offers "smoother" control than SpeedFan anyway.
2. AFAIK all GPUs ship with PWM fans, reference and non-reference to my knowledge. So, unfortunately, they don't stop spinning. According to this review
the quietest GTX 660ti runs at 1080 rpm in idle.
3. Obvs I have no answer here, but having run my much, much hotter reference GTX 470s without fans I can tell you that they will heat up fast under use (I hit the temperature limit/auto-off after only a few minutes of gaming). That said I don't see why a good aftermarket heatsink wouldn't do okay under typical loads, but I'd still expect to approach the 90s before too long, depending on your case airflow.