Well the check engine light has come on now. I had taken it to the freeway for a couple of miles, and also filled some gas.
I checked the manual and it says the light may come on after you have refueled the vehicle (due to loose cap etc), but since that has not happened before, and given the problems I had last 2 days, there must be something wrong.
So will take it to the mechanic now and see what needs to be done.
If there are any suggestions regarding this (check engine light and it's consequences etc), pls do let me know.
Thanks for all the help till now.
And yes, I did try to see if the steering can be maneuvered once the turn the engine off. I figured out that the extent to which it can be depends on the speed of the vehicles. Immediately after I turned it off, I could steer it well, and it kept getting "stiffer" as the car slowed down. When it came to a halt, the steering was really jammed, and I do think I will break it if I try to steer it at that point