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No, no FID, but you'll still need the FID to lawfully possess non-large capacity rifles and shotguns in MA, regardless of whether they are C&R or not.
To If you are buying out of state, the seller won't care about you having a MA license.
By law, all dealers are supposed to ensure that the transaction complies with Fed and State Laws. Thus, they should ask for your MA FID/LTC as well. If they don't they aren't complying with the BATFE requirements.
As Emoto put it so well, you need a MA LTC or FID to possess and/or purchase the appropriate class of gun (or ammo for same).
I'd love to see a carbine in SW500.
No, legally someone with an FID is NOT supposed to be able to buy ammo for a pistol. Some shops may ignore it while others may ask if it's for a rifle or pistol if all you produce is an FID.
Nothing prevents the buyer from lying however, so this is meaningless especially as damn near every pistol caliber is available in some carbine too.