Observers in two different inertial frames will measure the same acceleration of a movingobject. Will they measure the same velocity of a moving object? Will they measure the sameforce on the moving object?

No, they will not measure the same velocity of a moving object, but they will measure the same force on the moving object.
Consider two observers, one at rest, and the other one his car moving with uniform velocity of say 10 m/s east. Suppose at t = 0 s , both the observer observe another car moving with uniform velocity of east. To the observer at rest, the initial velocity of the observed car is 10 m/s east whereas for the other observer in his car, the initial velocity of the observed car is zero because both moves with same uniform velocity.
Later the observed car start accelerating eastward with an acceleration of say 2 m/s² . To the observer at rest, the observed car has reached a final speed of accounting for the acceleration above whereas for the observer in his car, the final speed of the observed car will be 2 m/s.
Therefore it can be seen that for both observers, one at rest and other in a car moving with uniform velocity of 10 m/s, the acceleration of the car they observer is same. However their perception of the velocity of that car is different. Force acting on the body is equal to the mass of the body times acceleration of the body. Since mass is a constant quantity and the acceleration of the car they observe is same therefore they measure the same force on the moving object.