I use gmail through the Web to check my gmail email account. A far as I know you cab only check gmail emails through gmail. If you have a bt email address you would need to log in through bt webmail (a webpage from bt that lets you check your email) or have something like Microsoft outlook installed on the tablet which would download your emails for you.
Gmail is great when you get used to it. I use to check all my email accounts, label which account the mail came from, filter messages into folders (gmail calls them labels), access my mail from phone, tablet and PC.
Setting things up I find is easier when logging in via a PC. Once setup, using app on tablet is fine.
I have dropbox on my Android phone and when I take a picture it automatically uploads it, so I can then view it or download it on my laptop. Works really well and you get quite a bit of storage for free.
Does she already have a BT Internet email address? She should be able to download an email client app that will work with this, although I know from dealing with my step-dad's recent foray into the world of tablets that BT Yahoo is a bit lacking in the standard features of an email service and can be hard work.
Alternatively as you've alluded to, you can get Gmail to act as a sort of gateway to the BT Internet email, which means setting up some stuff on Gmail itself (i.e. in a browser) and then the Gmail client should work out of the box.
For doing file transfer, the others are right - Dropbox is far simpler than messing about with wired connections between devices. For dealing with an Android tablet, Airdroid is my new find (new to me, already known to everyone else with an Android device, I'm sure!) which seems to work well.