Your mother's house would be just another ADSL installation. Depending on how their billing is organised, you or she could be the account holder, you or she could pay for it. Unless you will be the main user.
(Quick unofficial view.)
I think so. You would have another email account there with another username; your mother could have a "slave" email account. You could access your main email using a browser to Post Office and your main username. Your partner can forward email from home to you at your mother's house.
Would the new connection be for you while you are there or would your mother want to keep it?
Do you have good mobile reception there?
It may be quicker to increase the data limit on your phone and use a laptop tethered to the phone.
An ADSL connection will take a certain amount of time to install.