Your 1st conclusion is correct, i.e., only a prima facie case is needed to file a charge-sheet.
With regard to your 2nd conclusion, I may state that fresh material (as mentioned by you) can be filed in the court during trial with the permission of the court. Moreover, after filing of the charge-sheet, the police can conduct further investigation under the provisions of Section 173(8) of the Cr.P.C., wherein fresh material can be collected.
Your 3rd conclusion is correct, i.e., the role of the public prosecutor basically starts after filing of the charge-sheet, though as mentioned by me earlier, before filing of the charge-sheet he may be involved in bail matters and other miscellaneous matters connected with the case (such as return of property seized, for example) that are filed in the court during the stage of the investigation.
With regard to your query as to whether the complainant can ask his own lawyer to conduct the full case, it may be stated that if it is a “private complaint” case, it can be done. However, if the case has been instituted on the basis of the charge-sheet filed by the police, as a general rule, the trial can be conducted by the public prosecutor or the assistant public prosecutor in charge of the case. But, there are some limited exceptions to this general rule. Sections 301 and 302 of Cr.P.C. are relevant in this regard, which are reproduced as under:
“301. Appearance by Public Prosecutors.—(1) The Public Prosecutor or Assistant Public Prosecutor in charge of a case may appear and plead without any written authority before any Court in which that case is under inquiry, trial or appeal.
(2) If in any such case any private person instructs a pleader to prosecute any person in any Court, the Public Prosecutor or Assistant Public Prosecutor in charge of the case shall conduct the prosecution, and the pleader so instructed shall act therein under the directions of the Public Prosecutor or Assistant Public Prosecutor, and may, with the permission of the Court, submit written arguments after the evidence is closed in the case.
302. Permission to conduct prosecution.—(1) Any Magistrate inquiring into or trying a case may permit the prosecution to be conducted by any person other than a police officer below the rank of Inspector; but no person, other than the Advocate-General or Government Advocate or a Public Prosecutor or Assistant Public Prosecutor, shall be entitled to do so without such permission:
Provided that no police officer shall be permitted to conduct the prosecution if he has taken part in the investigation into the offence with respect to which the accused is being prosecuted.
(2) Any person conducting the prosecution may do so personally or by a pleader.”
In the above sections, I have highlighted the portions that are relevant to your query.