No. No matter how P moves, it moves between AB, where m is the midpoint of AP and n is the midpoint of PB. As AP gets bigger, PB will get smaller, so the length of MN will not change.

2. When point P is on the extension line of AB line, will the length of MN change?

Yes P moves on the extension line between AB, m is the midpoint of AP, and n is the midpoint of PB. In one case, AP becomes larger and PB becomes larger, which will change the length of MN.