I got my work permit card on Friday. Does this mean I can apply for a social security number now (or a tax ID number in the case of wanting to start a business)?

yes, with your EAD you can apply for your SSN.

Yes you can apply for your SSN now. My SSN took about a week to be processed. They need to check with USCIS to make sure all the details you provide are correct. I don't know what the situation is in your state, but here in VA, they dont really try to hard to contact you with the SSN so it took a few calls to receive the info.

Another question... am I correct in thinking that they wouldn't give me a work permit if they didn't intend on approving me at the interview?

The reason you apply for the EAD is so you can work while you're waiting for your green card.
My husband's SSN was in the mail in less than a week.

No, they would revoke your EAD if they decide to deny your AOS. An approved EAD doesn't mean a likely to be approved AOS application. Congratulations on getting your EAD and good luck with the rest of the process.