Listen to your gut. Look for another job. Be SURE you are secretive about it, though -- it's pretty clear that Dan, and probably the new manager as well, will find a pretext to fire you in a split second if they get wind of the fact you are job-hunting. Be sure to get a reference for your current work from someone you can trust, or, let any potential employers (at the interview stage) know that you are seeking a job while needing to keep the current one for financial reasons (if that's the truth), and refer them to someone who worked closely with you in your last job(s) before this one.
You're right that Dan seems odd. Especially as he has been nothing but unhelpful, and even illegal, in his treatment of you -- it was against the law for him to ask your age in the initial job interview. and he may have been skirting law when he refused to give you a copy of your contract. The comment about birth control from the other manager could absolutely be construed as harassing. Your bosses are going to be sued one day if they act like this to employees.
If you have any interest at all in staying where you are, you need to go to HR -- if the place even has an HR department or HR specialist. I have a feeling that this workplace either has an HR person who is doing those tasks while in another job, and so may not know much about HR law and regulations, or it has an HR person who might be tight with the bosses and who would not help you adequately, or would rat you out to them.
Frankly I might just decide that you're not coming back from the pregnancy. But take care on that. If your job provides your health insurance you cannot afford to lose your coverage in the late stages of pregnancy, and though you could possibly be eligible for COBRA coverage or coverage under the Affordable Care Act, you might not get the benefits for childbirth like you have now. Factor that in to what you decide. (If it were me I'd leave no matter what!)
Also be aware that if you job-hunt while clearly pregnant, while is IS illegal for them to discriminate against you based on that fact, such discrimination does happen, and if it's in their heads and never voiced, you cannot prove that you were denied a job because you were pregnant. Overall, I'd tough it out until the baby comes and then not return after the pregnancy. Sure, the current bosses you have will probably crow, "See? We knew she wasn't going to come back!" etc. since they seem to have an issue with pregnant workers. But you won't care because you won't be there.
Be sure you and your husband are stowing away EVERY spare penny in a good investment or other account because if you have an infant it may be tough to go back to work as soon as you might need to financially, especially as you must figure on child care costs.