For messaging we have 2 Facebook Messenger groups, one is for general chat and updates and is our primary way of communicating, the other is solely for sharing song ideas, progress, setlists etc so that's a much less busy thread and makes it easier to find things
Calendar wise I've used TeamUp for years after finding log in security problems with Google, which is fair enough to be fair. TeamUp gives one person the master link and everyone gets their own link, they can log in on a computer or use the app. Here's a screenshot of ours, blue entries mean someone is busy and can't gig, red is gigs, yellow is rehearsals. Like any calendar it's only as good as the information within it so band members need to take personal responsibility for keeping their details up to date. As an aside, when you open an entry there's space to put details such as which band member booked the gig, who with, agreed fee, contact details for the venue, timings of the gig.