1. Can a criminal case be brought against the LLP since its designated partner played an active role in influencing public to invest their money into 'Prime'
Action can be taken against the designate partner for his effective role.
2. Is the LLP deemed to have knowledge of the fraudulent acts of Nailesh and others by virture of the fact that Nailesh is a designated partner in the LLP.
The designated partner has acted in his individual capacity by utilising fraudulent means to usurp the funds.
3a. Is the LLP suo moto bound to take action against its partners once it has been informed by the public that its designated partners has committed fraud. L&T LLP is a subsidiary of L&T Group, a public limited company.
If the LLP found some actionable substance there is nothing wrong in taking suo motu action.
3b. Who are the legal obligations of a public limited company if its detects fraud by its managing director/ designated partner
Whoever acted against the interest of the public.
4. Is the LLP also liable if it does not complain to any authority about the breach and has not taken any steps to pre-empt anticipated breach? Can the LLP in such case be said to be aiding / shielding the fraudulent partners
No
5. Is the LLP also liable for the wrongful act or fraud of its partner which causes loss or injury to any third parties (Note: no money was brought into the LLP's account)
LLP cannot be held liable for individual's fraudulent act.
6. What kind of investigation can be brought against the LLP to investigate the role of LLP in the fraud
LLP can be implicated in the complaint
7. What are the legal remedies available to the investors against the LLP.
You may mention the reliefs sought for and let the court decide the same on merits.