Can I file a green card for my husband?

You can apply for a family based visa petition for your husband the visa most likely will be approved. The problem he has is obtaining residency. He will not be granted residency in the US because he entered illegally unless he entered on or before 2001 and qualifies for 245i. For him to obtain his residency, he is going to have to leave the US to his home country, go to the interview over there and present waivers for illegal presence in the US and a few others. This is a very difficult process and it is very hard to be given admittance back to the US unless you can prove extreme hardship to you and your child if he does not come back. Extreme hardship has a very high burden of proof, just because he was the financial supporter does not work. You are recommended to consult an attorney that can review all the details of your case to see if it would be feasible to go through this risky process.

Yes, your husband will have to leave and be outside the US for 10 years unless he can get a waiver of the 10 year bar to reentry by showing extreme hardship to a US citizen spouse, which is fairly difficult to do in most cases.

You may petition him but he may need to process the application in his native country but the unlawful presence waiver application could be processed in the US thereby shortening the time required to process the same in native country.

It depends on his exact manner of entry, any immigration filings that may make him eligible for section 245(i) relief, and any immigration or criminal violations.

You can petition for him and have him go through consular processing. He must file a waiver to get around the 10 year bar.

The answer is that it would appear that you can file a petition on behalf of your spouse. However, if he entered the US without inspection, sounds like he would be required to leave the US and be required to submit appropriate applications with the consulate and USCIS office abroad to obtain an immigrant visa to return. Before setting yourself on this plan forward, I would advise that you schedule a consultation with a competent attorney who can review your spouse's case, determine if he may qualify to apply for any immigration benefits in the US and if not, the process of submitting the applications thru the consulate. Be careful out there and make sure you hire someone who is both qualified and who can answer your questions and explain the process to you. Good luck.