I keep getting emails from subscribers that their account has expired, but their credit card was charged. When that happens I go to User Management ---> Subscription and reactivate their account from there. Hoping that it will sync the following month. Is that the right procedure?

You need to have a Grace Period set for your plans when using recurring subscriptions. It's not a guarantee that Stripe will process and notify your site that a recurring payment has occurred just before they expire. A Grace Period of at least 3 days is typically recommended.

Also in the Private messages, the trash can icon to delete messages has disappeared, so I can delete the PM anymore, any ideas what could have happened with that?

If you can delete the message it'll be on the dropdown menu to the far right. Hover over the 3 dots for the option. This assumes you're using the internal PMS model. If using UddeIM I've no idea why you can't delete.