Secrecy and non-disclosure are an integral part of any commercial relationship. The attorney-client relationship mandates the lawyer under a moral & professional obligation to maintain his client’s confidentiality.

Without a client’s expressed consent no barrister, attorney, pleader or lawyer is permitted to disclose any communication made to him in the course of employment as the communication which is made between a lawyer and client is a privileged one.

Indian Evidence Act 1872 has been designed solely to protect the client’s interest. So NO such NDA require.

no lawyer is going to sign any NDA 

communication between lawyer and his client is privileged communication and your lawyer would not betray your trust 

3) Without a client’s expressed consent no lawyer is permitted to disclose any communication made to him in the course of employment as the communication which is made between a lawyer and client is a privileged one.

• Yes, if he agrees to sign NDA, he can.

Yes, no hard in asking your lawyer to sign a NDA. Having said that, even if there's no NDA in place, I do not think your lawyer will leak the info you give out. The most basic principle underlying the lawyer-client relationship is that lawyer-client communications are privileged, or confidential.

You can but actually it's not needed.  A lawyer is bound not to disclose the facts to third parties

There is no rule. 

It's all about your trust and no advocate disclosed about a case on one client to any other

You cannot enter into any such agreement with any lawyer, if you are not confident about the lawyer change the lawyer.

No lawyer will agree for such condition to take up your case.

The information you give to your attorney is already a privileged information between the client and his attorney.  However, you can very well sign NDA with a lawyer.  

1. As per the information mentioned in the present query, makes it clear that you wish to execute a NDA for feeling safe in talking and telling everything about the issue.
2. Yes, you can execute the same and otherwise also advocates talk with clients are under the category of privilege communication, but yes the same is limited to law point of view.
3. You should go for the same as it will give the faith on both sides and would be good for future relation.