[c3] 20

ab*a | ba*b
a((bc|c)da)*
empty|ab*c

[c4] 20

see picture

[c14] 20

You could use pumping lemma or induction, straightforward.

[c15] 20

see picture
see picture

[c17]

The data structure and algorithm can be the same as for the DFA, with
just a few changes:
 - each entry in the transition table bring you to not just one state, 
   but (possibly) a set of states
 - use CLOSE on all the entries in the table
 - the algorithm maintains a set of current states, rather than just one
   current state
 - the "next state" is the union of all the entries in the table for the
   current states and the given input character
(There are also recursive solutions and/or solutions that use BFS/DFS,
 but most of these do not save space (and none save time).)

NFAs could be attractive because the number of states could be much
smaller than in the corresponding DFA.  A classic space/time trade-off.
Years ago, a small table might have had value so it could all fit in
memory at once.  These days a small table might help cache performance.