To Backup WLM data you'll have to find the folder where WLM stores it's data.
By default it is something like C:\Users\*username*\AppData\Roaming\Microsoft\Windows Live Mail
But in WLM you can set your own default folder, so if you can't find it, open WLM > tools (little icon with a window and an arrow)> options>advanced>maintenance>store folder
Inside the folder you find all kinds of subfolders.
If you want to be able to restore everything, just copy the entire folder to another location and your safe ;)
If you're looking for just the emails of a particular account:
there are folders with the name (or part of the name) of you email accounts.
I have one called "Hotmail" (very original, I know LOL LOL LOL), so I have a subfolder "Hotmail (se 742"
Inside are the subfolders for this account, like send, inbox, drafts etc.
In there you can find all the emails sent to and from this particular account.
So far I haven't found a way to 'export' contacts like you can in Outlook Express or Windows Mail,
but this is because contacts are also stored in the cloud, so whenever you login on another computer your contacts will appear there too.
Which makes me think yet again you'll have to get in the cloud (= go to hotmail.com of live.com or whatever it is these days LOL) to delete contacts ...
Let us know how you fare - still a subject we need to learn more about ;)