Here are a few hints to get you going, I'll post some more later tonight.
#1 - really just unit conversion ...
#2 - if you use energy & momentum conservation, you should come to a ridiculous conclusion. For instance, if you write the energy and momentum of the electron in terms of gamma, try solving for the electron's velocity ...
#3 - conserve momentum. The velocity will be very small (but measurable with the Mossbauer effect, which we'll get into later).
#4 - there is only one thing different compared to normal Compton scattering. It is that easy.
#5 - Rewrite the Compton equation substituting energy in place of wavelength appropriately. The energy difference E_i - E_f will be a function of E_i and E_f, and that is OK. Proportional to both, in fact.
#6 - just do what I suggested in class ;-)
#7 - from frequency and speed, you can get wavelength. The total energy per unit time is just power, which is the energy per photon times the number of photons per second. It is a stupidly large number of photons.
#8 - plot + regression ("trend line" in business-speak). Note that the slope of the stopping potential (y) versus frequency (x) gives you h/e, not just h! Multiply the slope by e=1.6e-19 to get h in familiar units.
#9 - you can use your result from #5. If the electron is initially at rest, its energy is just its rest energy. You want to find the change in energy divided by the incident photon energy. As we discussed in lecture, the energy shift should be much larger percentage-wise for higher energy incident photons.