Safety is pretty good. I would not worry about that unless you are schlepping 100k worth of diamonds or something. Normal precautions are advisable but you should not be overly concerned.

Definitely take the flyaway to Union station and the Red Line to Universal. The Red Line station is at the bottom of the hill that the hotel is on. Either take the shuttle or walk up. Either way will have you there in just a few minutes after exiting the station.