Tutor profile: Balram R.

Can a point particle be observed to be accelerating even when there is no force acting on it?

If the observer's frame of reference is not an inertial frame, even a free particle (i.e. no force acting on the particle) may be seen to be accelerating.

If we have a static distribution of electric charges contained within a spatial region of finite size, is it possible to estimate the total electric charge in that region by only measuring the electric field at a point that is very far from the core of the system?

Yes.

Are there quantities that are conserved, i.e. remain unchanging with time, in any isolated physical system? Give some examples of such quantities.

Every isolated physical system has some conserved quantities. Examples are: (1) Conservation of total Energy. (2) Conservation of total Momentum. (3) Conservation of total Electric Charge.