Can I appeal to her/court under Section 9 "Restitution of conjugal rights"
Not necessary, it is too early to initiate any legal action against her including a lawyer's notice,since it is only three months after she delivered the baby, you wait for another two months.
1. Is my demand to my wife to come and stay with me is correct considering my son is only 3 months old?
The above answer suit this too.
2. Is my demand to my wife's family member not staying with us permanently is correct?
If you do not like your wife side people staying in your house on permanent house, you have got all rights to ask them to leave the house, but if they had come there to help your wife during her pregnancy, it will be inhuman on your part to behave that way with them.
3. What can I do if my wife is not willing to stay with me?
You wait for some more time, let she first recover from her post delivery weaknesses and other related issues.
4. After child birth my wife is facing severe mental disorders like talking about suicide, not sleeping, not eating food, not interested in husband, hitting the kid sometimes and etc.. but I don't have any evidence for this. If i wish to file divorce under "mental illness" what are best chances.
After delivery you have stated that she is living in he parents house, how did you come to know about her such attitude, did you not inform her parents about this, if it is a continuous affair, you may consult elders and decide about either advising her or to lodge a complaint with the police that she is unnecessarily threatening you to commit suicide and blame you for that, hence to take your complaint on their records for first hand information in case she indulges in any such act in the later stage,this may help to protect you from any legal implication/onslaught in the later stage. Take wise decision.advise ofelders.
5. What is the best legal advise for me?
You have to wait patiently, in my opinion, this is a temporary situation which may improve on passage of time, allow her to recover, don't keep troubling her by provoking words through frequent phone calls or in person, she will be very tender now owing to her delivery of baby, so she has to be handled very delicately, hence avoid harsh behavior with her, as far as possible try to convince her and make some efforts to reconcile the issues, if she is still adamant, just ignore it, dont attend to her calls and maintain silence for a good period so that this will make her to realize and amend herself. Think and act wisely.