Hi jerseygirl15! You've gotten a lot of good answers from everyone. I thought I'd just summarize it and add a little more.
In your case, your Sim will have to do all of the proposing. The father of the baby won't do it on his own. When you get their romantic interactions high enough, you'll see the option to "Propose Going Steady" if there are no bugs in your game and you're patched up to the current update. Once you get this option and if he says yes, you can immediately propose marriage and get married on the spot if you're in a hurry. Otherwise, you'll just have to go through all the same interactions another time until you get back to the high level that gives you the "Propose Marriage" option. Once they are engaged, you can have a private ceremony any time by clicking the romantic options.
As for going back to work, maternity leave is up while the baby is still a toddler and cannot be left alone. You're only option if the mother is the only grown Sim in the house (teenage or above) is to hire a babysitter. If you try to leave the house for work without one, you'll get a message that the toddler can't be left there alone. And as already mentioned, if you get a message that the babysitter has to leave, just ignore it. The babysitter will stay until your Sim gets home from work.
Regarding the father and the baby, they will know that they are father and son, but the father may or may not interact with the baby. It will depend somewhat on the traits of the father. Don't expect much from him, though, unless he happens to have the Family Oriented trait. Once the baby ages up to child, he will be able to initiate interaction with the father and they can be friends.
I hope you've gotten the answers you need. If we've missed anything, just post it and you'll get lots of help!
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