Alice smashes the Bat-Signal, explaining why the one in Elseworlds looks different.
Tommy says to Kate he paid someone to "riddle" him the answer to Batman's secret identity, an obvious reference to Edward Nygma, aka The Riddler. In the comics, the Riddler figures out Batman's secret identity as Bruce Wayne and reveals it to Tommy. Armed with this information, Tommy (as Hush) and the Riddler team up to take Batman down.
"Candy" or "Candy Kane" was Kate's cadet nickname in the comics; here, Tommy Elliot calls her the same thing.
Alice tells Kate that the red she is sporting on the Batwoman symbol, the lipstick and wig comes from the color of their birthstone. In the comics when her father gave Kate the suit, Kate notes "red and black...gevurah, the pillar of severity...the colors of war."
Rachel Skarsten learned the cello in secondary school; that really was her playing.