You can definitely move a site between servers. This is the primary use case, and the reason this software exists. It's just so happens that when you transfer a site to the same server… it's a backup! People are more likely to look for backup software rather than site transfer software – even though ours is both – which is why we market it as backup software.
It's funny that you said "if one day one of my servers burns down" because this is literally what many of our clients used their backups taken with Akeeba Backup for two years ago, when OVH's data centre went up in flames due to an electrical fire caused by a faulty UPS battery unit. Our clients who where religiously taking backups of their sites, storing them on off-site storage (outside of OVH) were able to restore their sites on a different host and resume business as normal. We had quite a few thank-yous coming our way.
Regarding the first two problems, edit your .htaccess file and remove everything that's not part of WordPress' own .htaccess. If you don't know how to do that, there's an option in the upper right hand side of the Site Setup page of the restoration script.
Regarding the last problem, it sounds like you are trying to restore on top of an existing site. It's best not to do that. Remove all existing WordPress files and folders, and use an empty database to restore. This way you can be sure that anything already present on the server won't interfere.
Nicholas K. Dionysopoulos
Lead Developer and Director
🇬🇷Greek: native 🇬🇧English: excellent 🇫🇷French: basic • 🕐 My time zone is Europe / Athens
Please keep in mind my timezone and cultural differences when reading my replies. Thank you!
