With regard to Pelikaan beer:
On the French side you can find it at Monoprix at Bellevue. It is also available at the Carrefour supermarket on the way to Philisburg. You can also find it at Liquor and Amsterdam Cheese Shop (near Chesterfields)

Apparently, you can also find it at the following restaurants: Sao in Orient Bay, both restaurants on Pinel, Plongeoir & wine bar in Marigot, and on tap and bottle at Lagoonies (I understand the owner of Lagoonies is the owner of Pelikaan). We looked for it at Blue Bitch Bar in Philipsburg but they didn't have it. But on our way ome we found it at the Blue Bitch Bar in the airport.

Regarding Dinghy Dock:
They seem to have specials everyday. Sometimes days, sometimes evenings. On Sunday, craft beer is half price.

The gate:
It was open when we were there in January... in fact, there was no actual gate at that time.

Chairs at Pedros area:
As mentioned, Cedric has the Club O chairs. Colin is also renting chairs next to Cedric on the south side of the rocks. On the north side there were also chairs for rent between the rocks and Kontiki. The going price when we were there was $20 for 2 chairs and an umbrella.