Hi Michelle,
1. No; atomic radii is not required knowledge for the MCAT. If its needed, it will be given. MCAT is more of a critical thinking test than a regurgitate information test :)
2. Alkali earth metals are less reactive than alkali metals because of Zeff (effective nuclear charge). As it moves to the right of the table, the radii of the atom decreases, due to a closer proximity to the inner core positive protons, the atom itself will be less reactive (since its less likely to want to lose those electrons, making the atom super positive).
3. I am sorry, I am not sure where this value is from for Zeff = 1ev. Can you be more specific on what question/page you saw this on? Thanks!
4. Actually, it does. Zeff = Z - S, where Z is atomic number and S is the shielding constant. Its not necessary knowledge on the MCAT though. You just need to know the trends of Zeff.
5. I would memorize the light constant (3.0 x 10^8 m/s). As for Planck's, I have seen questions that doesn't give the constant, and questions that do, so the answer is... maybe. Its one of those last things you want to do and memorize, just in case.
6. For this question, all atoms has the same number of electrons, but different numbers of protons. Therefore, with an increase in protons (positive charge), and the same number of electrons (negative charge), the Zeff would increase, and the electrons would be pulled closer to the center of the atom, and thereby resulting in a smaller atomic radii for the atoms with larger atomic mass (with more positive charges but same number of electrons).
7. Nomenclature is not super duper important. We will get more into it in organic chem, and the instructors should point out what is important to know :)
8. Sorry... I am not sure what you are referring to. I have checked the Study Guide questions, ICE, AAMC, and CC resources for lecture #1, Question #2, and I have not found what you are referring to. Please let me know the page number and also resource name and I can assist you further.