Is this sentence is correct or not?
How many petition a player can file?
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Sign up to join this communityNo, it is not correct.
How many petitions {can a player file}?
You needed to invert the subject-verb order of the {marked clause} (and enlist an auxiliary verb).
What time {does the train depart}?
When {will you come home}?
What food {does the iguana eat}?
How much wood {can a woodchuck chuck}?
P.S. But your use of the article a is correct.
The article "a" is correct, because it goes with "player"; you are talking about any single player.
However, there are two mistakes in your sentence:
How many petitions can a player file?
Note that without the question mark, the word order would be valid; for example in a list of key facts, you might write:
How many petitions a player can file: 10
Which is another way of saying:
Number of petitions a player can file: 10