A.) No. There is no separation. You can’t be separated if you are living in the same house. Furthermore, any “agreement” without your signed, notarized signature is invalid. He couldn’t have filed it with the court. He is lying to you.
Furthermore, the attorney is right. DO NOT SIGN ANYTHING, ANYTHING WITHOUT HAVING YOUR ATTORNEY LOOK OVER IT FIRST. Once a separation agreement is signed, you are obligated to it. Courts consider a separation agreement to be a private contract and are reluctant to interfere or change anything.
B.) Yes, once you separate, you are the dependent spouse and he is the supporting spouse. That is how it has been for the last 11 months, so that is how it will be seen. He will be asked by the court to provide support for you. If he refuses, you can file a motion for post-separation support.
C.) Child support should start immediately upon separation. Use the calculators on this site to figure out the amount. If he doesn’t voluntarily pay it, you can get a court order to enforce payment.
It is in his best interests legally to go ahead and pay child support and at least some modicum of post-separation support. If he refuses to do this, it will not go kindly for him when it comes down to facing the judge later.