Breakdown of situmon ga arimasu ka?

Questions & Answers about situmon ga arimasu ka?
In this sentence が marks the subject whose existence you’re asking about—“Is there a question?”
Using は would make 質問 the topic (“As for questions…”) and imply contrast or a known topic, which isn’t the focus here.
あります is the intransitive verb meaning “to exist” (for inanimate things).
So 質問がありますか? literally asks “Does a question exist?” but functions as “Do you have any questions?”
か is the question particle that turns a statement into a yes/no question.
Without か (質問があります), it’s a plain statement (“There is a question”). Adding か makes it “Is there a question?”
In Japanese, to ask if someone “has” something inanimate, you literally ask if that thing “exists” for them.
So Xがありますか = “Does X exist?” = “Do you have X?”
Insert 何か (“anything/any”) before 質問:
何か質問がありますか?
This reads “Are there any questions?” or “Do you have any questions?”
Yes, ありますか is polite/plain. For extra formality, use ございますか:
質問がございますか?
Use the plain form and drop the question particle:
質問ある?
This roughly means “Got any questions?” and is common in casual speech.