As to your other questions (oops, forgot about those
), whether you have an encrypted file system or not does not matter for somebody that tries to gain access remotely. Any file that you have you access, somebody else can access remotely if they gain access to your system while you are using it. An encrypted file system is to prevent somebody that has physical access to your computer from accessing your files.
If during installation you had selected to encrypt your home folder, the files would be encrypted always on the hard disk, but once you are logged in the operating system lets you transparently access these files. So if you are logged in, and your backup program is reading files that are encrypted on the hard disk, the operating system transparently unencrypts these files for the backup program (or whatever other program access the files). It's not to prevent you from doing anything with your files, it's to prevent anybody else from doing anything with your files while you are away. And again, somebody access your computer remotely while you are using it can access these files because you are logged in...
Linux Mint comes enabled with some services to facilitate interoperability with other computers in your home, but those services are not accessible outside your home. You don't need a firewall for that and so Linux Mint doesn't enable it by default. Some more details about these services and how you are not at risk at home, here: viewtopic.php?f=29&t=103992#p599112
. You can enable your firewall (ufw) easily and you can disable some services if you don't need them (see the link in the post I linked you to). To enable your firewall, open Firewall Configuration from the menu, Unlock it, slide status to ON, and set Incoming to Deny. That's it, you can close the Firewall Configuration now and you don't need to open it again unless you want to change some firewall rule.