Yes, I am Infinite...
Grrrr, Who Said Yes?!....
There is technically an infinite amount of "points" between any two positions, so yes.
The amount of points is irrelevant.
If these point do not have size, then yes. If these points do, then no, even if it were possible, which is up for speculation.
Yes, it is not only theoretically possible, it is basically the fact of our reality. The Universe is...well..infinite. And motion can exist. One would never reach the beginning or the end, but it is the case and motion does exist.
There is a limited number of points in the space, otherwise it would take forever for moving from point A to point B.