Q: "Two people playing on a basketball court in the city." Does this mean that "There are people playing basketball"?
A: yes

Q: "A beautiful young lady sitting on a stone." Does this mean that "A fairy sits on a rock."?
A: it is not possible to tell

Q: "A man cooking rice on a brick stove." Does this mean that "A man with a large pot cooking rice on a stove."?
A: it is not possible to tell

Q: "Two men holding skateboards and one man skateboarding." Does this mean that "A group of friends play a board game in the living room."?
A:
no