i don't know how to describe the relationship between surface tension and the shape of a liquid drop. Also what are the attractive forces that increase surface tension?
The free energy is minimized by minimizing the surface area. For positive interfacial energy, that corresponds to a sphere (in the absence of gravity). For negative interfacial energy, that corresponds to mixing- *maximizing* the intrfacial area.
The atomic origins of interfacial energy are murky, to put it mildly. One need not discuss atoms to discuss dividing surfaces.
Depends on where the drop is - is it on a surface? Cohesion due to intermolecular attractions answers your second question it is your responsibility to find the list of such attractions.
Then factor in adhesion-also research the topic of contact angle-the more the liquid molecule is attracted to the surface the less spherical it's going to be.