Email aliases are not accounts, they are simply additional addresses which deliver into the inbox alongside the main address. You access them with the normal account ID and password - you can't sign in with them. The Mail app and the iCloud website allow you to specify an alias as the 'From address'. Many email clients also allow you to specify a 'From' address which isn't the account's actual address, and that would be what you would need to do to send as from an alias.
Note however that to sign into iCloud mail from a non-Apple application you will need an 'app-specific password' in place of your normal iCloud password. In order to do this you need to set up two-factor authentication for your Apple ID, and for this you need to have either a Mac running El Capitan or above, or an iOS device running iOS9 or above.
Two-factor authentication for Apple ID - Apple Support
Using app-specific passwords - Apple Support
If you are unable to set up two-factor authentication you should set up 2-step verification and use that to create an app-specific password (see link below) . Then go to https://appleid.apple.com , select 'Password and Security'; click 'Generate an App-Specific Password' and follow the instructions. Once you have the password, copy it and paste it into the password field in the application instead of your usual iCloud password. You should also keep a note of it (though you can generate a new one if required).
Two-step verification for Apple ID - Apple Support
You will need to nominate a 'trusted device' - any phone capable of receiving SMS messages. There will be a 2-day wait before you can complete the process.
(A particular caveat (about 2-step only) - you will be issued with a 'Recovery Key' in case you lose your 'trusted device'. Make sure to write this down and keep it in a safe place; if you lose both it and your trusted device you will be permanently locked out of your ID. You'd be surprised at the number of people who've posted here that they've got themselves into just that position.)