Part of the initial formation of question is completely vague. If, you want to file an application against the Government in relation to any grievences, you can file it. There is a distinction between an application and a Civil Suit. If a suit has to be filed, it can be filed before the civil court of the Competent jurisdiction. If the suit is for a mere declaration, a notice under Section 80 of Civil Procedure Code is mandatory, but it the suit involves urgency or the relief prayed is involving emergent nature of the relief, a suit can be filed even without notice, but with an application under Section 80 (2) of CPC, requesting the Court to waive the notice under Section 80 of Civil Procedure Code.
If, you have any cause and would like to file a matter before Honourable the Supreme Court, you can file it, if at all there is anything in the form of the findings or judgments to be challenged. Since the full facts are not placed here by you, it would be little difficult to answer it completely.
As far as appearance is concerned, any lawyer duly enrolled in any State Bar Council can appear and plead his case, but instructed by an Advocate on record. An Advocate on record can only file Vakalatnama.