Child's first British passport from abroad

hello, I'm a naturalized British citizen, my son was born abroad after my naturalization which makes him British by descent. I would like to apply for his first British passport, but I have a few questions so that I get it right first time:

1 Can I apply from the UK where I live or I have to apply from the country where the child resides?
2 I'm registered on his birth certificate as the father. Am I deemed to have parental responsibility or the mother? (mother and I are not married but we are in a relationship) Can I apply on the child's behalf?
3 I have people living in the UK who can counter sign the passport application form. They've known me for years and know my son through pictures but have not met him yet, because he lives abroad. Can they countersign or it has to be someone who has met the child physically?
NB: My partner is not British, at present, she lives with my son in my son's birth country.

Thanks very much.