You can have many accounts. Moments has been replaced by Photos (much better). Personally, I wouldn’t hassle with running an email server. I use mailbox.org

Yeah, backup is very easy, I backup to a locally attached external hard drive as well as to a cloud service. There are loads of options and ways to manage backups

A single bay “J” model should be around $200 including a 4tb drive. You can achieve a lot with that, especially if your focus is automated photo backup

Nextcloud, as mentioned, is a great option but does require a bit of work, albeit not much. I would recommend a Synology server. They’re fantastically simple and this was my approach after trying Nextcloud. I did this to divorce myself from Google. Synology has many mirrored services