Depends on where you are traveling from. if you are traveling from Bus or train, you can get down at Hospet and take an auto rickshaw from there to Hampi. Auto rickshaws are a good option to roam around in the city while on the other side of river which you have cross by boat, you can hire bikes for which you need to carry, driving licence and some other Id proof. there are many resorts to stay at and many eateries. you'll love Hampi if you love scenic beauty.
Thats a tough one my friend. It could take you anywhere from an hour to maybe three. Much depends on traffic and jams. So plan in a manner that you have sufficient buffer in hand. Usually Ola/ Uber apps could give you indications on travel time. You could also look up Google to tell you how long it is taking from Howrah to Dum Dum on your travel day around 10am. That might help you guesstimate.. Best of luck.