Apply for ILR in case of European family member death

Hi I came in this country on a student visa and my mum and brother came on a visit visa. My father was a Dutch national. In 2008 we applied as a European family member and we got 5 year visa in 2009. Unfortunately my father passed away this year. My questions are ;

1. Can we apply for ILR in case of my father death ?
2. Some one told me that if we apply for ILR then we don't need life in the Uk and ESOL B1 certificate( in European case)

Can someone please advise me ?

Many thanks