I think you should take the baby and leave him, for three reasons:

1) that he is not excited about having a newborn baby is very disappointing. I am really sorry you ended up having a baby with him; men who are not excited about babies (with some exceptions - there are men who honestly cannot connect with babies and can only connect with older children, but at least they are aware of it and wish they were different but they cannot help it - in your situation, it sounds like your husband does not feel that his not being fully engrossed in baby care is his deficiency) are not worth your time, in general. While I can understand that he might have been bored or whatever or seeking approval from those various women on FB before, with a 6 week old baby...

Does he carry your son in a sling? does he change his diapers? does he bathe the son? what does he do? from your post, it seems that you are doing all the baby care and he uses his phone and his BF to connect with various women... which sounds pathetic.

2) he said to somebody that he was not married while he was married. This was meant to mislead two women - you and the other woman. He tried to misled her into believing that he was not married. He also tried to mislead you into believing that things were not the way they actually were. I do not think that such a severe case of dishonesty is treatable via counseling, so, in my opinion, counseling will be a waste of time and money and an extra reason for your getting more and more bewildered.

3) he does not like your FB pictures at all. This is so pathetic. I mean, if it does not occur to him by his using his own bright mind that he should at least like your pictures as frequently, if not more, than he likes the pictures of other women, he is a hopeless case.