1.What are the precautions should I need to take to make sure they do not come back and bite me later?
The steps you have to take will consist of their assurance in writing that they will not demand any amount in the future including alimony or maintenance after closure of this case. This can be recorded in the court records.
2.Can the existing HMOP of the contested divorce be converted to mutual consent petition ?
This cannot be converted into mutual consent divorce, however, by filing a memo stating that you submit to the decree prayed for her without allegations, the court will decide and decree dissolving the marriage by a decree of divorce.
3. Should I have them drop the ongoing case and file a fresh petition for mutual together?
Not necessary, the above step can be followed, you can give instructions to your lawyer accordingly.
4. Just withdrawing the current case will end the court proceedings for this HMOP or is there any specific procedure to dismiss the case be followed?
question repeated in another form, replied already.
5. If they don't drop the case initially and the negotiation fails, typically how long will it take to move to the evidence phase in the ongoing contested case. I have just filed the counter petition one week back.
If the negotiation fails, since you have already filed your counter, trial of the case will begin in the next hearing itself.
While negotiating the terms, do not budge to their pressure, lest you will be stranded with more and more demands from their side.