"Planets rotate east-to-west"? That's not a cliché, it's a tautology.
It's a terrible way to phrase it, but "west to east" rotation is prograde. "east to west" rotation is retrograde.
Not in ordinary English. Dictionaries usually define "east" as to be the direction that the Sun rises from [at equinox].
Yes. And if a planet rotates from west to east, the sun rises in the east.
It's a dumb way to put it though. Planet rotate anticlockwise around their north pole. If the north pole is pointing "up" (axial tilt is 0-89°) that means the sun rises in the east and sets in the west. If it points "down" (91-180°) then it's still rotating in the same direction around its north pole but seen from "above" it now looks like it's rotating in the opposite direction (so the sun rises in the west and sets in the east).
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