There are several different types of events! Generally, the events don't give you cards and only offer items to level your existing cards up, but they're also valuable items!
Most events do have required EX songs, but Hoshimegu didn't because the staff wanted the story to be easily accessible. You'll get used to it, I promise!
I missed hoshimeguri and that made me sad but thank you!!! There is just a lot and I wasn't sure how events worked because the wiki had a lot of types of events and I was so confused