There is a parking entrence fee to get into the park. It is $7 on weekdays, $10 on weekends. Cars with a disability placecard or licence plate are able to get in for free, though it does look like you need to sign up ahead of time using this link: https://www.dcr.virginia.gov/form/DCR199-036.pdf After you get into the park, there is parking next to Powhatan Hall which is where the reception is held.
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The park does allow for dogs but they have to be with their owners at all times. And the reception hall does not allow for dogs unfortunately. There is no extra fee for dogs staying on the campground but there is a $10 a day extra fee for people staying with their dogs in cabins.
Yes! There are camping cabins along with yurts available for rent. https://www.reservevaparks.com/Web/#!park/25 Look under "Pocahontas Sites" for camping cabins, and under "Pocahontas Campground" for yurts.
Camping cabins: Fits up to 4 guests. Linens are not provided. Guests must bring sheets, pillowcases, blankets, and towels. The cabins themsleves do not have bathrooms inside but are located near bathrooms with showers. They do have electricity but no heating. Yurts: Fits up to 3 guests. Linens are not provided. The yurts do not have bathrooms but are located near them. They do not have electricity.