Not really. However, you should have a general idea as to what a generic amino acid looks like (NH2-CHR-COOH, except for glycine, which is NH2-CH2-COOH. Also, amino acids exist in their zwitterion form in the cellular environment at the physiological pH of 7.4) which amino acids are polar, which are acidic (aspartic acid and glutamic acid) and which are basic (HAL or histidine, arginine, and lysine).
i think you should know what's special about the three unique amino acids (cys, gly, pro) and like others said in general what types are acidic, basic, polar, nonpolar. design your own mnemonic and move on to other materials
unnecessary. the only ones you should know for sure are glycine and maybe proline. however, I'd know the pKa values for COOH and NH3 (the COOH is around 2 and the NH3 is around 9). this helps with determining protonation states in solutions of different pH values.
if you had the additional time i'd just try to semi-memorize which amino acids belong in which category (i.e. nonpolar, basic, acidic, polar, etc.)