In the case of a horizontal motion, if the push force=resistive force, will the ball even move, let alone move at constant velocity? ???

[/quote]

The original starting condition determines the outcome of the motion.

your answer is true if the initial velocity = 0.

however, it is agreed by the physics community that if the initial velocity of the object is non-zero, it will continue in the state of motion due to the evidences of data with real life experiments.

so even if the push=resistive force at the beginning,

using Fnet = m*a

P - f = m*a

0 = a

but v is the starting velocity, thus it could be still traveling at some speed without any direction change [color=blue](this will happen but not likely to be observed because it is an idealized motion)

[/color]

to extend this knowledge to real life situation, you could relate this to a ice sledge on very smooth ice horizontal ground.

when the ice sledge is already moving at constant velocity, say v=10 m/s

ideally does not require any pushing force to continue at constant v

in the presence of air resistance, P - f = m*a where f >0

if P =0

then -f = m*a, therefore, it will -ve = a and it will decelerate. [color=blue](this is observed in everyday life motion)[/color]

in this case, to maintain v = constant,

P - f = m*a

P- f = 0

P = f so a small Push P of equal magnitude to f is required for Constant v [color=blue](this is observed in everyday life motion like the motion of say a bicyle in constant v on horizontal ground)[/color]