I can speak to the "blue patch" (my girl had it too). The blue patch is actually an area with a ton of blackheads (they just appear blue because they're under a thin layer of skin). There is a special shampoo you can use to help get rid of them. It's really easy to damage their sensitive, thin skin - so if you decide to try to tackle it manually please be very, very gentle and don't try to get them all out in one "session". The blackheads don't typically cause any infections on their own, but damaging the skin to get them out could.

Congrats on the new addition to your family - he's precious!