I have audio recordings of a Skype conversation with someone who might become my legal opponent. Is there any reputable institution in India that can test and verify these recordings to ensure they haven’t been tampered with?

In India, accredited laboratories under the Ministry of Electronics and Information Technology (MeitY) can examine audio recordings for authenticity. You can contact MeitY to get a list of these labs, which can conduct forensic analysis and provide expert reports on the integrity of your recordings.