How much email can the Webmail hold?

Your webmail (AtMail) is not designed to hold all of your email forever, you ideally should download your email to your local computer when you have a chance.
Webmail is ideal for if you need to check for emails when away from your usual pc, or out of the country.
The more email that you store within your webmail will limit the speed for accessing your email, and also this amount counts towards your disk space site usage.

What is my SMTP outgoing email server?

If you host with UK-Cheapest then already set up on your account for you is an SMTP Outgoing email server address of the following format,

Replace with your actual domain name.

However, some ISPs will not allow you to use your own SMTP server through their internet connection. In these cases they should allow you to therefore use their own smtp server which they provide to you.

If they will not allow this either, then you will need to contact them to remove the block they have placed on you using your own smtp server. See Which SMTP Server should I use?

Known companies that often block include BT and AOL, it appears that Nildram allow you to use your own server.