The other replies are pretty good. 1. To migrate I'd use their email import utility. I've never used it but I've heard good things. On the Fastmail side set up

The other replies are pretty good. 1. To migrate I'd use their email import utility. I've never used it but I've heard good things. On the Fastmail side set up sender identities so you can compose (and reply) to emails using your @gmail.com address [if you're using gmail addresses]. On gmail side you can continue having a dual email setup by having gmail setup forwarding such that it forwards the email and keeps a copy in gmail. I have 4 gmail accounts setup this way, so I know that I can always fallback to gmail if there's an issue on Fastmail (haven't had one for over a decade with this setup though). 2. Fastmail indexes emails so they're searchable via their web UI. It's pretty good, I've not really had any issues. In my opinion, the best way to use Fastmail is to bring your own domain. One really cool thing about Fastmail Web UI is that it integrates well with catch-all email addresses, so you can have <catch-all-alias>@mydomain.com and when you get emails to that address, when you click Reply it automatically sets your sending identity to <catch-all-alias>@mydomain.com. This ensures your correspondence is consistent with the email aliases you use.