Can we bring firewood for the firepit ?

Yes you can bring in your own firewood, I would recommend it. Most Jellystone Park sell it as well, it's not overly priced but it does add up if you're using the wood every night.

Yes

We always buy it across the road.

yes but they also sell it there. Of course it can get pricey buying it there. several homes outside of campground that sell it also.