adoption or custody? HELPPPPP

Hi, I had an annulment but unfortunately the custody was not tackled which means that me and my ex husband had the legal custody with my daughter. Eversince, my daughter grew up with me and never did his father supported him financially and emotionally. Family ko ang nagpalaki sa daughter ko. Now, May new husband na ko and baby. Hindi sya Filipino citizen and we're applying abroad para mag migrate. Payag naman ang dad ng baby ko na ibigay sakin ang custody pero d ko alam ano ang means and ways para masimulan and how long will it take? and how much na din? willing ung dad nya na ibigay sakin since hindi naman nya inalagaan and pinalaki ung baby. ANo ang best way para maka produce ako ng legal document certifying na sakin ang custody ng bata? Thank u so much

and another thing, hindi pala kami kasal ng partner ko now, i was wondering if allowd na i adopt nya baby kahit d pa kmi kasal.

Naaawa kasi ako sa bata dahil ung case nya pinagaaralan pa ng embassy and di pa lumalabas, malapit na kami umalis since na grant na ako ng visa, ayaw ko naman iwan magisa ang anak ko dito sa mga parents ko dahil nasanay na sya na kasama kami ng kapatid nya. Mas mapapabilis sana ang case processing if may document ako with regards sa custody nya dahil nagask ung embassy if kelan sya mag tuturn to 7 sabi ko this year na kaya hindi na ata nila kinonsider ung automatic custody since malapit na sya mag 7.
Thank u in advance

was this a 'no appearance-package deal annulment' or you actually appeared in court?