Correct on both counts. Since they don't indicate any solvent, you are merely deciding based on the stereochemistry and how substituted the carbon is.
i) tertiary carbon indicates Sn1 chemistry, the fact that they drew stereochemistry and then got rid of it, indicates that likely you have a racemic mixture which would arrise from an Sn1 substitution
ii) primary carbon, inversion of stereochemistry are both classic signs for an Sn2 reaction (although not exclusive)
I don't know if you needed help with the other parts, but I've provided some info. The compounds D and E are easier, let me know if you need help. Remember where the double bond in a hofmann elimination reaction is going to show up.
for C:
for compound C, we have a good leaving group Br- and a nucleophile (the lone pair on the nitrogen)
for D: this is just a google search