Your crating schedule sounds pretty good actually. It's a lot better than my dogs got as puppies.
Yes, take him out right away when you get home, and carry him outside it that's what it takes to avoid an accident. As he gets older he'll be able to hold it longer.
We started out with the puppy crate in the bedroom and slowly moved it farther away as the puppy got older. It seemed to work well. Keep in mind your puppy is still very young and is still getting used to his new home so it's normal to not want to be alone right away, especially at night.
Yes, take him out right away when you get home, and carry him outside it that's what it takes to avoid an accident. As he gets older he'll be able to hold it longer.
We started out with the puppy crate in the bedroom and slowly moved it farther away as the puppy got older. It seemed to work well. Keep in mind your puppy is still very young and is still getting used to his new home so it's normal to not want to be alone right away, especially at night.