Am I required to work if I want to legalize my husband?

More information is needed to really answer your question. Family income and savings can be used.

You are not required to work but you are, as a petitioner, required to submit an affidavit of support showing that you have sufficient income/assets. If you do not, because you are not working, you will have to get a joint sponsor (anyone who is a US citizen or US permanent resident and whose assets/income is sufficient) to sign the affidavit of support on behalf of your husband.

Without a more detailed information about your situation, I am unable to give a meaningful answer to your question. I;d need to know for instance your own immigration status, your husband's status what visa does he presently have that expires in November. Assuming you are a US citizen and wish to file green card for your spouse, there are a lot of things to consider. With respect to finances, one of the requirements is that you show CIS that if given a green card, your husband will not end up on welfare. If your financial situation is such that you cannot convince CIS, of this, you can always find a friend or relative who is financially capable to join you in filing co-sponsor affidavit. There may be other issues in your case, but absent a clear understanding of your situation, I will suggest that you consult with an immigration lawyer. The money spent for a good consultation is money well spent and will save you thousands of dollars and sleepless nights down the road

You do not have to work, if someone who does helps you by serving as a joint sponsor. There may be other options.

If you wish to petition for your husband and do not meet the income requirements necessary to sponsor him, you may obtain a joint sponsor who can help you meet those requirements.

No, you can use a co-sponsor for the affidavit of support requirement.