Answer 1:
On a rotating perfectly radially symmetric planet (non elastic!) you will weigh more at the poles because your weight is mg and m is the same for you but g is higher at the pole than at the equator because of the outward force at the equator that vanishes at the pole. Now on a real planet, the polar radius is smaller than the equatorial radius because the earth is ductile. Hence the figure of the earth is NOT spherical but instead oblate spheroid with two diameters equal in the equatorial plane and the polar radius shorter. So although you are farther from the COM at the equator (hence pull weaker) there is more mass underneath you (pull stronger) and I am not sure if these two effects cancel out. But still thats not the real Earth which has differences in density nonradially... so my guess is that the effect of spin will be most important and you will weigh less at equator than at poles. You can look up gravity maps or in particular the acceleration due to gravity at any location on earth and that would answer the question. Weight is higher when g is higher since your mass is constant.
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