It's easy riding a bike here, much better than in California... of course, you can ride the sidewalks, just be aware that Singaporeans don't watch where they are going... at all. I've been stopped at the crosswalk waiting for the light to turn and had them walk into me.
The cops here don't go against bikes at all. Just the other day I was riding in lane two against traffic (past the cabs at Centrepoint), and a cop went by without even looking at me. If you think I'm nuts, I used to be a bike messenger in San Francisco... so i'm qualified (don't you try this).
Bikes are an excellent way to avoid long bus/mrt rides, taxi hassles and traffic jams. It helps if you have a shower at the office if its a long way, but for just getting around... they're great... I even bought a three wheeled trishaw (wagon in the back) so if you see a white guy on Orchard riding a red three wheeler... thats me!
As for leaving your bike parked on Lavendar for two nights... duh! Thats near Little India, the locals there need bikes to use and sell... so if it wasn't just parts getting stripped its the whole bike... the solution (if you must leave out overnight there) is to get an functional but ugly bike... no value, right?