tongtong,
Not dangerous lah, but JB being JB, need to be more careful lor, eg, always lock the door, never leave the engine running if driver leaves the car, try avoid going to places at night time if you are not familiar with the place, etc.
We usually reach Singapore custom before 9am. So far so good. Even if there is traffic, only need to queue for <30min, so not too bad. Try to go as early as possible, if you can reach Singapore checkpoint before 8am, almost guarentee no traffic jam (long weekend excluded).
JJ Tebrau City is definitely a safe place. And you would be amazed how many Singapore cars you can spot there. Oh, the car wash at the JJ is very good, but long waiting time. If you are not satisfied with JJ, move on to Tesco, just next door. Shopping centre usually only open at 10 - 10.30am. If you are early, go to a local coffee shop for breakfast first. For lunch, can easily settle in JJ, lots of restaurants for you to choose from.
If you are planning to go to Toy R Us, it's worth checking the price at Singapore first to do a comparison. I remember the Playskol walking car I bought in Singapore cost me about $80-90, that day saw it at JB, only RM120 (something like that).