You are right that FastMail doesn't send out invitations when using third-party clients. FastMail is mentioning it on their page [1] promising they'll implement it, however I think this should not be the job of FastMail, but that of the client. For example this works fine in Thunderbird because Thunderbird sends those invites by itself, all you need to do is to specify which email address is linked to which calendar. Thunderbird sends invitations by itself for regular CalDAV accounts, but with a Google Calendar it doesn't do that because it is Google's Calendar that it is special. In this case it is the CalDAV-Sync integration that should send the invite.
Mobile Firefox is new and it doesn't surprise me that FastMail's compose doesn't work in it, because it has weird behavior when I interact with text boxes. I also use Firefox on my Android, but not for mobile web apps. It's currently too unpolished for that. But I'm sure that some bug reports will help.
One thing I'm happy about with FastMail is that things improve. For example they weren't supporting CardDAV for family accounts before August. Now they do and I'm pleased with it, though I wouldn't mind some extra functionality.
But that's the thing we are missing in the consumer / producer relationship, the direct relationship between the parties involved, the feedback. With Google there's nobody I can talk to, because they are too big to listen to individuals like myself. Usage of Google, Apple or Microsoft products leads to much like what happens in agriculture ... the rise of monocultures, the end of diversity and ultimately we end up with disastrous consequences for our own health.
