How can I determine whether rust has made my bike unsafe?
Sounds like you have only surface rust. The frame would have to rust through to cause any integrity problems and that would take many years of damp conditions. The creaking you hear when shifting your weight to the bars may be the headset. 

It may be worth getting it serviced. As its likely the grease has escaped/become clogged with dirt causing the creaking. It would be wise to check all the joints and welds for signs of fatigue or cracks. Ensure they are all solid.