At which entrance is the easiest and quickest to enter the park if I am staying at the BW Stovall's Inn??
Sorry, there is no "quick" way now to get to the Turnstiles from the BW Stovalls now. The shortcut that allowed you to cut through the Grand Californian Hotel, through Downtown Disney is now gone, as that Hotel no longer allows anyone through their Main entrance except guests staying at the Hotel, and you have limited access through the Downtown Disney access as well at certain times getting back into the Hotel. Now its about a 21 min walk or so as you have to walk basically to the Disneyland Hotel, and through Downtown Disney that way as there are new Security to get through even to get into Downtown Disney now.
If you have to stay there, I would suggest just taking the Art shuttle service that has a stop at the BW Stovalls and expecting that to take approx 30 min.