1. Do I have any other option to check whether this incident is coming up during a verification or not?
This will not come under verification since this is a petty case and the police will not maintain records of such petty cases once it is disposed with fine
2. Can I obtain a Character Certificate (I already have a passport) without citing any reason?
From Where? police?
Dont do any such mistake, who is police to certify your character.
3. Should I declare that I was arrested and convicted?
Dont do that, you were actually not arrested, just detained and were let off on paying fine, even otherwise you are not knowing if there was a case filed or fine paid, it is a matter of three years ago.
4. Even if I do so I have no document, no case no - nothing with me, and as per the rule I have to give these details.
Dont bother so much, dont declare or reveal any such details.
5. Where can I get these details?
In the same police station
6. If I don't declare this incident will it come up during background verification?
This will come under any verification report
7. Can this be a hindrance to my opportunity as I don't want to let this opportunity go.
If you are frightened about this petty issue and declare then it may make an adverse impact, better dont reveal anything in this connection in any application form