Applying for EEA2

Hi Guys,
I have overstayed my visa and i'm planning to make an application using the EEA2 form. Me and my partner have been together for 1 year and 5 months and we started living together in August, 2014. I am a non-EU but my partner she is an EU national. She just gave birth to twins in August. Not sure what my chances are so why i have decide to ask a couple of questions on the forum. My partner is Lithuanian

1. I have an old passport which has expired which carries the visa i came into the country with which has expired as well. When I am making my application, should i provide the home office with the old passport as well or just the new one?

2. Since I and my partner have not been together for 2 years and cant proof a durable relationship, what are my chances? At the moment the only utility bill I have is the TV licence of our new place in my name. Is that good enough? And how important is proof of address in making an EEA2 application?

3. Mentioning the babies in my cover letter, will that help my application?

All advice and responses will be appreciated.

Thanks guys