2000 Toyota Corolla Steering wheel vibration and brakes squ

Hi

My 2000 Corolla has around 137 K miles on it. It is a stick shift ( manual transmission).
Off late I have noticed a vibration / jerk pattern which I can sense in my steering wheel.
It drives fine at all speeds ( These days I have tried up to 65 mph), But I have seen some things that concern me.

1) I have felt good amount of vibration in the steering wheel off late. I am guessing that the vibration is present always, but I am not sure if I can differentiate it from nominal vibrations in this car. The vibration is least noticeable when I am accelerating from 0 - 35/40 mph and most noticeable when I put the car to neutral and break while slowing down for a light. I also feel that the car halts quicker than normal, when put on neutral without applying brakes.

2) The car quickly drifts to the left when the steering wheel is left to itself.

3) Some kind of vibration is felt in the foot as well.

4) When the car is still, and on a slightly downward slope ahead (neutral without hand brake or leg brakes applied), I guess the car doesn't move but I occasionally hear a noise. This noise is very similar to one that we hear when hand brake is applied initially to park a car on a slope.

I am not sure what is going on. Any ideas?

Also, I would appreciate if I could get some idea about how much it would cost me to fix it.

Thanks
Raja