hiya and Congrats!
Yes, your child will have dual citizenship, whether or you want it to. after you register the birth and get the birth certificate you have to register it with the us embassy, you can do the passport at the same time. There is a thread on this that is stickied (on my phone and I can't paste the link) called something like registering birth abroad thingy (sorry it's not a more precise name) that gives all sorts of info about it.
With regards to the maternity pay, I'm not sure how this works when on flr, but someone will be able to tell you I'm sure.
With regards to CTC and child benefit, your hubby can claim these.
Pengi.