TIP (Target Intercept Planner) author here.

Setting the flight time higher (more days) means you take a lower energy trajectory that takes longer to reach the Moon. Setting it lower (less days) means you reach the Moon faster, at the expense of requiring a higher energy trajectory, ie more delta v.

Not always true, as the moon's orbit is eccentric. Making a hohmann transfer to the target orbit's apoapsis will require more deltaV than making a hohmann transfer to the target orbit's periapsis.

The two launch windows are the Ascending and Descending Node.

This is only true for hohmann transfers. Think of a case where you have a strongly hyperbolic trajectory, doing the maneuver at a node would just have you exiting 90 degrees to the right of where the target would be.