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1. Have the continents truly moved apart? 
Apparently yes. There is considerable evidence that the continents have moved in time.  The matching shapes of the coastlines of Africa and South America have been discussed since the mid-1800s. Not only the shape, but the rocks sometimes match on corresponding continents.  There is also evidence that the ocean floor has spread apart between Africa and South America. 
2. When did the continents move apart?
Evidence for movement of plates seems present throughout much of the geologic record. The present configuration of continents is attributed to break-up of a large super-continent, Pangaea, which, in conventional terminology, started in the Jurassic. Continental movement continues today, although very slowly. Most creationists interpret Jurassic sediments as deposited during the Flood, so it seems the continents may have achieved their present arrangement during the Flood.
3. Does mention of the division of the earth in Genesis 10:25 refer to plate tectonics?
Probably not. The biblical context is the "table of nations" that spread out after the flood. The text most likely means that the land was divided among these groups of people. 
4. Does Pangaea represent the pre-Flood world?
Pangaea is the name given by geologists to a supercontinent apparently assembled toward the end of the Paleozoic and which began to break apart in the early to mid-Mesozoic. Most creationists believe these intervals of the geologic column correspond to a record of the Flood. Consequently, the formation of Pangaea would have occurred, in this view, during the Flood. The disposition and extent of pre-Flood continents may have been significantly altered by plate tectonic activity during and after the Flood. There is a need for more research in relating plate tectonics to the Flood.
5. How could the continents move fast enough to rearrange the whole surface of the Earth during the year of the Flood?
It may not be necessary that all plate movements were completed during the Flood; significant plate movements might have continued for some time after the Flood. The plates move very slowly at present, but might move much faster given appropriate conditions. A large amount of energy would be needed to initiate plate movement; perhaps this could have been provided by extraterrestrial impacts.  A lower melting temperature of the basalt rocks would have facilitated plate movement; it is known that the presence of water in basalt lowers its melting point.  It is not known whether plate movement might have been facilitated by the "waters under the earth" or the break-up of the "fountains of the deep," but this possibility is worth considering. Some creationists have proposed a theory of rapid plate movement that may provide some answers to this question.  The main proposal is that as tectonic plates subducted into the mantle, friction generated large amounts of heat The heat partially melted the undersurface of the plate, reducing the friction and facilitating more rapid subduction, which generated more heat, increasing the rate of subduction, etc. One problem with the model is that such rapid plate movement would heat the plates so much that it should take a long time for them to cool.
6. What unsolved questions about plate tectonics are of greatest interest?
When and how rapidly have the plates moved? What happened to the pre-Flood continents? How could the ocean-floor magma cool in a few thousand years if the plates moved so fast during the Flood? 
 Snelling AA. Plate tectonics: have the continents really moved apart? CEN Technical Journal 9(1, 1995):12-20.
 See, e.g., Harris, C et al. Oxygen isotope geochemistry of the silicic volcanic rocks of the Etendeka-Paraná province: source constraints. Geology 18(1990):1119-1121.
 Consult any standard reference on historical geology for details.
 The Hebrew word, eretz, often means “the land,” although it can also refer to the entire planet Earth.
 Glikson AY. Asteroid/comet mega-impacts may have triggered major episodes of crustal evolution. EOS, Transactions of the American Geophysical Union 76(6, 1995):49ff.
 Thompson AB. Water in the Earth's upper mantle. Nature 358(1992):295-302.
 Baumgardner JR. 1994. Runaway subjection as the driving mechanism for the Genesis flood. In: Walsh RE, editor. Proceedings of the Third International Conference on Creationism. (Pittsburgh, PA: Creation Science Fellowship, 1994), 63-75.
 This problem was raised in: Barnes RO. Thermal consequences of a short time scale for sea-floor spreading. Journal of the American Scientific Affiliation 32(2, 1980):123-125. The problem remains unsolved, but some interesting work on related problems can be found in: Snelling A. The formation and cooling of dykes. Creation Ex Nihilo Technical Journal 5(1991):81-90; Snelling AA. Rapid' granite formation? Creation Ex Nihilo Technical Journal 10(1996):175-177; Anonymous. 1996. Queries and comments. Origins (Biblical Creation Society) No 21(1996), 22-23.