What force causes the induced EMF of a loop? And, the difference between a loop EMF to motional EMF?

If a loop of wire is placed perpendicular to a changing magnetic field, there is an induced EMF such that the induced current is flowing in a direction to create an opposing magnetic field like this simple diagram: While a rod(or wire) moving in a uniform magnetic field experiences a magnetic force pushing the positive charges upwards to create an EMF like this diagram: Questions:

1) The rod has a magnetic force due to it's motion in $B$ that causes the induce EMF, for a changing magnetic field perpendicular to a loop (like the first diagram) is there a magnetic force as well creating the induced EMF? If not, what is the force(s) causing the induced EMF?

2) For the motional EMF of a rod, by increasing the velocity how does it increase the induced EMF? The expression $\epsilon = -vBL$ is simple but imagining it is confusing. By having more charges? For a stronger E field?

3) If the rod is moving in a non-uniform magnetic field is it considered a varying B field? Is the formula for motional EMF valid? My approach is to calculate $B$ at certain points of $x$ and use the formula. Is this valid?

4) This relates to the first question, for this diagram: A loop moving in a uniform $B$, has an induced EMF = 0, because of EMF's of each side of the wire cancels out like so: Also they are in series, for me it's easier to imagine those wires as battery sources all of equal potential opposing one another. Why isn't this similar to the first diagram Of a varying $B_{\bot}$? The rectangular loop moving in a magnetic field has zero EMF, while a loop in a changing magnetic field has a non-zero EMF, why aren't the sides canceling out?