Depends when. There aren't actually any physically single cabins - they are just twin cabins with one bed folded up - but I've travelled on the ferries a few times where only disabled or premium cabins have been left. These are typically around peak school/public holiday times.

You can travel on the day, but I'd do a test booking with Stena to check the costs. However, the easiest way is generally to book directly with Stena online or by phone, and I believe they'll refund your train fare when you pick up your tickets at the ferry terminal.