For W-4 (Step 3) my girlfriend (dependent) child (6) has lived w me full time since 3, not blood related but I mainly pay. Can I claim as qualifying child or just other?

Ran out of room on original post -- I pay nearly all costs for the child (naturalized citizen) and the biological father is MIA/restrained from the child. Mother is claimed as a dependent and does not make enough to file. Can I still claim or does she simply not meet criteria for qualifying child dependent (2000 sum instead of 500 as "other dependent") because she is not blood related nor adopted at this time?