This is my understanding: There were Two Holiday.
Holiday #1 -- Gilda, Dent's wife, was the first Holiday -- Just like she admitted in the last four pages. Dent promised that they would spend more time together when he had less work, so Gilda spent three holidays murdering members of mob boss Carmine Falcone's gang. I suspect that she gave up the murders on New Year's even when Roman's son Alberto Falcone was murdered, assuming that Harvey took up the role of Holiday.
Holiday #2 -- Ablberto Falcone faked his own death, becoming the new Holiday. This plot was hatched by Alberto and his father, who both decided to use Holiday to take out men of rival Boss Maroni.
As for why the Riddler lived on April's fool's day, the Roman hired him to "solve" the Hiliday case and publicize the fact that the Roman was "looking" for Holiday. Alberto as Holiday, "failed" to kill Riddler in the alley -- who else but a family member would even know about such an alley.
After Alberto was caught, he confessed to ALL of the holiday killings. Making himself to be a bigger criminal than his father.
Yes...she says "I"all along. The thing that confuses things is that Gilda says to Dent that he took over after her from New Years Eve, however this is where Gilda is wrong. She thought it was Harvey when it was actually Alberto who took over. harvey was never the Holiday killer (if u don't mean he turned into Holiday when he killed Falcone).