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If you are following the path of one of the circles of dots, the magnetic field is uniform because the dots in the circle are evenly spaced, so there shouldn't be any change in flux.

Which image are you talking about? I meant this one:

The diagram in the question is showing a side view of the Earth, but for a plane going around the equator don't you need to look at a top down cross section (which is what I drew)?

If you look at the cross section of the Earth cut through the equator then the magnetic field is into the page. If you travel around any of those circles then the magnetic field strength would be constant. How can you have a change in magnetic field strength without a change in magnetic flux...

Yes, the field lines are vertical, but the spacing between them changes as the plane goes from north to south, so the magnetic field strength should vary. If you're going east to west, isn't that like moving a metal sheet within a uniform magnetic field? You only get eddy currents induced when...

The cut off part of the question says "Four identical planes are flying above the equator at the same time with the following speeds, directions, and altitudes." The correct answer is C, but I would have thought that going east to west around the equator at a constant speed and altitude there...

Think about what happens to the rocket's mass from the perspective of planet X. (and remember F=ma)