I don't have these issues with Fastmail + custom domain, but you need to make sure that DKIM and SPF is set up correctly. Fastmail helps you to check and fix this.

My issues were with Zoho, with DKIM and SPF set up correctly. Would be interesting to see if the domain (or top-level-domain) or the e-mail provider is at fault. It's difficult to test given the number of signals that are involved in flagging a message.

That seems very odd. There's no reason why mail from any domain with good mail servers should just land in spam folders. You should investigate. Perhaps someone is sending spam using your domain?