I have no idea about hiring cars in Orissa. I always travelled by train or taken the travel car from Calcutta. From Bhubaneshwar to Cuttack it is around 45 kilometers.

I don't think so as it will be monsoon in August and the sea is quite rough there

Yes one can very well go to Puri in monsoon. It is fun to enjoy the Puri beach during rain

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

Puri has two primary attractions, first - Temple of Lord Jagannath and second - Puri beaches. It depends upon your primary focus to visit Puri. That said, if you have decided to visit in August, I would recommend that you should visit. It is a call of Lard Jagannath and Temple door are always open to welcome people. Sea could be a bit choppy in August and violent but I am sure you will be careful. Weather could be hot and humid and do take umbrellas for the family. Best wishes for a great vacation.