When a marble is dropped into a beaker of water it sinks, why are all these wrong explanations? -the surface area of the marble is not large...

Surface tension can hold up objects that are heavier than
water, but only up to a point.  A marble is so heavy that, in order to float it via
surface tension, you would have to roll it out into a very large, very thin sheet. So
choices 1 and 3 don't really make sense here; surface tension forces are way too small
to have much effect on a marble.

Choice 2, comparing the
mass of the marble and that of the water, does not make sense either. Boats weight much
more than a marble, and they float. Also, the mass of the water is unimportant - an
object that will float in a glass of water will float just as well in a
lake.

Choice 4 is just a variation of choice 2 - neither
the volume nor the mass of the water matter.

What does
determine if something will float or not is its buoyancy. Buoyancy is determined by the
weight of fluid an object displaces, and this comes from the volume and mass of the
object itself, not from the water.  To determine if something will float, you must
compare the mass of displaced water and the mass of the object. For example,  If  an
object displaces 10 grams of water, as long as the object weights less than 10 grams it
will float.

In the case of a marble, which is made of a
dense material in a compact shape, the marble will outweigh the water it displaces, and
it will sink.