Hi Keeley,
I am not a lawyer and can not provide legal advice. That said...
Are you in the UK? Here is some general information on the
data protection act.
Generally speaking there is limited support for free email accounts and I doubt you can convince Microsoft to provide mail logs related to your email account.
You may be able to get an IP address login history by posting
here.
If there has been a a crime, or suspected crime, contact your local law enforcement to get their opinion.
to Email Questions!