It is not clear from your message as to whether you are the complainant or the accused, though it appears that you are probably the complainant. Secondly, it is not understood as to why do you want to check the status of the FIR from the court, i.e., whether the copy has reached the court or not.
Presuming that you are the complainant, please note that a copy of the FIR is required to be given by the police to the complainant free of cost immediately after the registration itself. For this purpose, Section 154(2) of Cr.P.C. is reproduced below, which lays down this requirement:
“(2) A copy of the information as recorded under sub-section (1) shall be given forthwith, free of cost, to the informant.”
So, if you want to have a copy of the FIR, you can take it free of cost from the police station itself, which is your statutory right (presuming that you are the complainant). In case you have a doubt whether the FIR has actually been registered, you can clear this doubt by demanding a copy of the FIR from the police station, instead of waiting for the copy of FIR to reach the court and then take a copy from the court.
With regard to your query as to in how many days the FIR reaches the court, the answer is: “it depends”. In the city police stations, where the court is situated in the same city, the copy of FIR should generally reach the court on the next day or may be in 2 days. This is the expectation, though in practice, it may sometimes be taking more time due to inefficiency in the system. If the police station is a rural police station and the jurisdictional court is in a different city, then also usually the FIR should reach the court in a couple of days or so (may be a few days more, sometimes).
Once the FIR is registered, it is the duty of the police to investigate and submit charge sheet or closure report, as the case may be, depending upon the result of the investigation. Of course, investigation may sometimes be delayed and faulty. You may ask the police officer concerned about the fate of the FIR or progress made in it. Generally speaking, they may share information with you if you are the complainant.