DL should be able to give you the WS PNR so you can access the reservation on the WS website or app
I flew WS (booked as WS) last week LGA-YYZ-LGA, and was offered the option to purchase seats; there were a few coded "L" for "less desirable" -- last row, and non-reclining row ahead of the overwing exits -- that were available for free, and basically the entire seat map save for "Plus" (first 4-5 rows with blocked middles) opened up at OLCI
as for TSA,
here's my experience at LGA last week ...