Although NaOH is not specified, the Claisen reaction does require some type of base. My main point was that when you're pushing arrows, you always point the arrows from the electrons/nucleophile to the protons/electrophile. So in your case, the arrow should be pointing from NaOH to the alpha proton, not vice versa. Like I said, it's a minor point, but I've known some professors who are very picky about that.
For C, you've started with the wrong starting material, you need to use diethyl malonate. C2H4 is also not an electrophile. You have the right general idea, but it needs a little cleaning up.