Yes

You can as many properties are operational now. Try Empire Hotel, Puri in Balia Ponda, on the beach (only a road between hotel rear entrance and the beach). Good property with helpful staffs--hopefully you will enjoy your stay.

The other answers look adequate.

Puri bus stand to Swargadwar is a short distance. Unless you have old people travelling, you don't really need to book a bus. Tell your group to take rickshaws or autos - both are available in plenty. By the way, how are you reaching the bus stand? If a bus is dropping you there, you might as well ask the bus to drop you off close to the Swargadwar instead.

Typically you can't, I mean if you want to spent whole night with beer in your hand and sleep over like Goa, but you can go to the beach any time you want, I went there around 2.30AM and stroll till 4.00AM, but yes cops and lifeguards will irritate you to the core and not to forget about the stray dog. Beware of them at night. P.S: There are many budget hotel just opposite to puri Bech, get one and enjoy the beach fullest

Good enough other than for the occasional rains

I clearly do not recall but yes... whatever they ask for is highly negotiable.

I'm at Mayfair Waves with a gorgeous view of the pool and the sea - amazing!

Call the hotel and ask.