Can momentum change?
Of course!  We see this all the time; football players tackling each other, car crashes on tv, and lots of other examples.
It takes a force to change momentum.

How much force does it take to change momentum?
This is perhaps not a very good question because any newly applied force will change an object's momentum somewhat.

Look at it this way... what if we change an object's momentum over time?...

Saying this in math terms, we have  Dp/Dt, which is the same as Dmv/Dt.

Looking at the units alone, we have Kg*m/s/s, which equals Newtons!

Therefore, we have F = Dp/Dt

If we isolate the "Dp" term, we have Dp = F*Dt, the F*Dt part is called "impulse".

Auto engineers are very familiar with impulse.  Why?  If a car crashes into a wall,  the kinetic energy of the car diminishes rapidly.  Thus the momentum also diminishes rapidly.  Dp is a constant, so engineers try to make the "Dt" as large as possible, therefore making "F" smaller.
How do they accomplish this?  They make cars with "crumple zones" which are designed to crunch like an accordian instead of being rigid in the crash.  Air bags serve the same purpose: make Dt bigger... it's much better to hit the airbag and have a bigDt with a small Fthan it is to hit the steering wheel with a large F and small Dt