Which state?

Nebraska

I only worked for a month and a half before giving birth this year...

Your state does not recognize common law marriage.<a rel="nofollow" target="_blank" href="http://www.ncsl.org/research/human-services/common-law-marriage.aspx">http://www.ncsl.org/research/h...>

Thank you

How much did you earn?  If you made less than $4,050 total for the year then he can probably claim you as a dependent on his single (or Head of Household) return.  Then you would still file your own return for your income but check the box that you can be claimed on someone else's return.

Nebraska is not a common law marriage state. Therefore you must each file your own individual tax returns. As for the children, assuming you lived together the entire tax year and the children lived with you, only one of you can claim each child as a dependent on your tax return. It's usually more tax advantageous for the one with the higher taxable income to claim the children. This is no problem if you and the BF are the biological parents of the children.

For direct deposit of any refunds, the name(s) on the account must match the name(s) on the electronic refund checks. If they do not, then the bank is required by law to reject the refund deposit back to the bank. So one of two things needs to happen.

 - Your BF opens his own bank account with his name only on it (recommended since he is not married)
 - You add your BF to your bank account, thus making it a joint account. (Not recommended for the legal problems caused if you two ever have a falling out.)

No, you cannot file a joint return if you are not legally married.  

If you live together, you  are allowed to split the children any way you want, 3-0 or 2-1. You are allowed to decide between you how to do that. Only if you can't agree, are there rules that who has the higher right.

Although the higher income parent usually comes out better claiming all the kids, that's not always true. The only way to be sure is prepare returns both ways and compare. This tool can be used for that https://turbotax.intuit.com/tax-tools/calculators/taxcaster/?s=1

The parent with the highest income needs to claim at least one child to file as Head of Household. The lower income parent must file Single.