Hi S.,
I have been there. If the only reason he is requesting 50/50 is to save a little child support, the judge should notice that. Has he already responded through the courts that he is requesting 50/50 or is he just telling you that? He may just be talking A LOT...they do that. Everyone is correct in telling you to keep a journal. Keep a very organized journal with dates and times and include anything in writing from him you posibly can, letters, notes, or emails. Then you will have to prove your case to the judge that you feel this is purely out of spite and for the purpose of saving money. You will need to stress that he has not spent time with the baby and shows a lack of interest until the child support issue came up.
Try to back track (in writing) and show the courts how often he visited the baby and if there were any broken promises regarding the baby.
However, brace yourself, you always have that chance that the judge could decide that he should have his chance at caring for the baby. Does he have a home, room, carseat, etc for the baby? Is the baby nursing?
As far as conducting yourself...respect the judge! Be sure to address him/her with "Your Honor" or "Judge". Stay focused on the babies needs and concerns. And, speak to the judge, not the babies father. Do Not engage in an argument with him, if you disagree with him, state your plee with the judge, that is who you are convincing.
Bring copies of doctor bills, hospital bills, child care etc that you may not have already given to your case worker.
Good Luck!