On 1, I'm not quite sure what your prof is looking for. We know carbon bonds to itself in relatively strong bonds and we know diamond has the face centered cubic structure with four tetrahedra inside a unit cell. Thus carbon corners are held together as well as each face is bonded. That explains why it is hard but not necessarily why it occurs as chunks. We also know that it cleaves very nicely along the planes because of the cubic structure. We know it comes up in volcanic pipes and the force of the eruption plus abrasion along the way may cleave large pieces into smaller pieces. I may be answering the question a little backwards; my point is that they were formed in larger pieces but cleaved on their way to the surface or as volcanic ashes were eroded to leave the diamonds in smaller pieces.
2. Graphite occurs in sheets. Air is adsorbed (not absorbed) on the surface of graphite. The sheet formation makes it easy for one layer to slide across another.
3. Fullerenes are large molecules (as compared to many others); however, they are not in the same league as diamonds. Furthermore, fullerenes crystallize in pentagonal or heptagonal structures that fit together to form the "buckyball." There is nothing to hold one buckyball to another buckyball; therefore, it is more likely to occur in powder form. In fact, soot contains some fullerenes.
Check my thinking. Do some research of your own and use that plus the above to make your own decisions.