1. I don't think the number you send makes a big deal, but I think it might be better for you if you send them one at a time. Feedback can help. Unfortunately, response time for NYT is very slow, but if you send to LAT you would hear back in time to make a difference on later submissions.
2. My understanding is that solvers and editors don't like quote puzzles unless they are LOL funny, or really appropriate. Frank Longo still does a lot of joke puzzles on Sundays where the first 4 or so theme entries are the set up and the last one is the payoff, and I enjoy those very much as a solver. Of course, Frank Longo is one of the real geniuses of construction.