How did you meter to get 1/90s, f/1.7, ISO200? Or did you just pick those out of the air? That seems like it would be underexposed by quite a bit in a low light situation. Perhaps Photoshop (or whatever you used to convert the RAW file) automatically boosted the exposure for you, which would of course result in grain/noise.
Quote: I don't understand how I can better expose when I was already @ f1.7
This comment leads me to believe you really don't understand how the three exposure parameters work. Pick up a copy of Bryan Peterson's "Understanding Exposure". It's a quick read and would probably help you understand this problem. In a nutshell, to let more light hit the sensor, you could have used a slower shutter speed, or increased the ISO. I'm regularly at ISO800 with my FA 50mm in low-light (and at f/2.0 or f/1.4) to keep the shutter speeds up.
The purple cross is a hot pixel, any competent RAW converter can remove them, and you shouldn't see them when you convert to a JPG anyway.