Watermelons take a fairly long season so don't expect them to be done early. Pumpkin leaves are tall so they would tend to harm watermelon vines growing together.

Watermelons don't usually put down roots on the runners...but can if covered with a shovel of dirt at a point along the vine. Water is needed mostly nearer the center of the plant.

Thanks Wayne. So do you suggest I plan on growing them at the same time but in separate areas of the space?

Yes, I wouldn't mix them together. Pumpkin vines of most types are very long so plant them where they can wander out of the planting zone.

Is it OK to plant watermelons and pumpkins in the same field in regards to cross pollination and flavor?

They don't cross pollinate, but as wayne said pumpkin vines are bullies. If they compete for the same space, the pumpkins win every time.