UK SETTLEMENT FOR MY SON AND I

[mary16]

I am on two year post study work permit that is due to expire in the next 3 months or so. I have lived legally in the uk for the last 7 years and previously lived 4.5 years in Europe.
I also now have a one year old boy whose father has ILR but has refused to apply for his british passport as we are now separated.
My question is

1. Is there any way that i can apply for my sons british passport.
2. Can i apply fo an extension to live in the uk given that my son has a right to british citizenship.
It would be very difficult for me to return to uganda having studied. worked and lived here and now have a son.

Please advice.

Many Thanks.