Hi there,
Yes, you should file Married Filing Seperately, and put 'NRA' for your spouse's SSN which stands for 'Non Resident Alien.' You can also put 'Non Resident Alien' for his name. TurboTax will continue to bug you about the fact that it's not a number, but it'll work fine.
I'm not sure about the rest, as I claimed the foreign earned income credit having lived here for a few years, but you may be able to claim it for the months you worked here by using the de facto method, not the physical presence one, as you moved here on a spousal visa with the intent to settle here. Best to check the US embassy's IRS site for more details.. No, your husband doesn't need to file anything.
Hope this helps.
-Stuart