My opinion on your queries are as under:
1. Whether a live-in relationship is legally permissible for my case when my mutual divorce petition is still pending ?
Opinion: No, it is not permissible, It comes under the Adultery and your wife may file a criminal case under section
497 of IPC 497. Adultery.—Whoever has sexual intercourse with a person who is and whom he knows or has reason to believe to be the wife of another man, without the consent or connivance of that man, such sexual intercourse not amounting to the offence of rape, is guilty of the offence of adultery, and shall be punished with imprisonment of either description for a term which may extend to five years, or with fine, or with both. In such case the wife shall not be punishable as an abettor.
2. Can my wife take any legal actions against me if she comes to know about my live-in relationship ?
Opinion: as above
3. What legal precautions I should take to save myself from any likely legal harassments from my wife ?
Opinion: Try to convince her for second motion proceedings & get divorce decree from court.
4. Can I marry my friend in temple (without registering) before my mutual divorce petition gets over ?
Opinion: No, it will not be better option for you.