No. The problem doesn't inherently lie in the possibility of having an "infinite number of questions" (which is a good problem to have), but lies in the narrow subject matter, wide scope, and low potential of usefulness these questions (in the forms above) present.
1) Asking about a specific player narrows the subject matter to one participant in any given sport. This represents a question that is rarely likely to be useful.
Alternative: Perhaps there is a specific technique utilized by a given player that makes him/her successful that can be captured and analyzed. This kind of question, which would not be about the player but about the technique, would be on-topic here as it would be useful to participants.
What does [player X] do that contributes to his high-percentage in converting penalty kicks?
2) Requesting information on a specific player (eg, Who is Lionel Messi?) is too broad (wide scope) and a research request. What about Lionel Messi do you want to know?
Alternative: If you want to know about a specific technique utilized by Lionel Messi, that would be a technique question and would be useful to participants.
How does Lionel Messi curve or bend the ball so sharply?
In response to comments above, a question like, "Is it true that Lionel Messi scored at least one goal for 66 consecutive matches?" cripples the scope and potential usefulness of such a question even further. The answer is either true or false. If false, the difference would be in the number of consecutive matches.
Alternative: Ask the trivia question, "Which player holds the longest streak for scoring at least one goal?"