No. According to Mike's post here, transponder 15 can feed spotbeams 1, 3, 5, 6, 9, 10, 12, 13, 14, 16, 18, and 21. I believe those numbers correspond to the old Rainbow spotbeam chart (also posted by Mike123abc), and not to the spot numbers reported in the uplink reports.
Apologies for my cryptic "No" above, prior to my editing. Now fixed.
As for your 2nd question, I think it quite likely that you are in a usable part of the NY spot. It's not strong here, but I can get it too in northern VA. That is, unless I'm seeing TP15 in spot 5.