When you are viewing an email or when you have checked emails in the inbox, you can choose various options from the action menu (circle with 3 dots button) in the top of the screen.

To move an email to another folder in the same email account, select 'Move to mail folder' folder from the action menu and select a folder.

To copy an email to another email account, choose 'Copy to email account' in the action menu. This options may appear in the 'More' option in the action menu. Then you can choose the email account and folder.

You can use 'Move to email account' in the action menu to move emails into a different email account which will then move the original selected emails to the trash.

To save emails as files, you have two options. You can choose 'Move to file' or 'Save as email file' in the action menu when selecting or viewing an email. These options may appear in the 'More' options in the action menu. (circle with 3 dots button)

You can also move emails to a folder or email account automatically using Email Rules (View). The rule can search for various fields inside the email and then move an email to a selected folder.