The features you list sound like something that should be implemented by an email client not an email host. I realize they have their own client, but that is really just a means to an end as it is obviously not their core business.
On top of that, it sounds like you really want something other than email.
Once you've used a service like Intercom, FrontApp or even Google's "Inbox" you realise emailing can be far more productive. It's a shame that companies like FastMail gave up on trying to improve the experience.