I had fun collecting flowers... sad that it's over already. Is there a list of the periods when events run?

There aren't concrete set dates, but Masquerade is next up in approximately mid-May. You can see the full list of holidays and approximate run times via the Subetapedia's holiday schedule

Masquerade doesn't have floating items like the Vesnali flowers. You'll have the option to request a dance with another user, and then when they accept (or if you accept dances that were sent to you), you'll both get trinkets. You have to have an item with "mask" in the name on your HA in order to dance. There might be some items that are allowed that don't explicitly have mask in the name, but any item that DOES have the word should also work