Mutual consent divorce

Marriage is not dissolved after a separation of three years.       Don't hazard second marriage without proper divorce.

If there's mutual consent, the separation needn't be mentioned.

HIV.    I'm ignorant of this subject.

There is no new law that marriage get dissolved if you are living separate for 3 years, the person who gave you this information has no knowldge of Indian law.

Secondly in order to dissolve the marriage easiest way is by divorce by mutual consent for which you both need to file joint petition in the Family Court and request for dissolution of marriage by decree of divorce. after waiting period of 6 months you get divorced by the Family Court. You may even jointly request for condonation of 6 months period of waiting for divorce as expceptional grounds exists in your case of 9 years of separation between both of you and Family judge may consider this and dissolve your marriage at earliest.

Mutual consent divorce is best option for quick divorce as explain above. In addition to above you may also file divorce petition as she is suffering from HIV +.