Question -How do you know the difference between evil Jinn's doing wrong to humans and people who are suffering from mental illness and who are behaving "weird"? I mean who is qualified to tell the difference? And to complicate the matter what about someone who has mental illness and also who are attacked by jinn?

In all of the above cases is the person responsible for his actions. And if he get back good does he have to make amends?

Answer

I think the ones who are experienced in dealing with the cases of Jinn possession and other related issues would know and be able to tell the difference. Anyway, I found some speech of Shaykh ibnul 'Uthaymeen related to this, he says in Fatawaa Adh Dhahabiyyah:

"...in his Zaadul Ma'ad, ibnul Qayyim mentions two types of epileptic or mad fits: spiritual (what which is caused by the Jinn) and physical (that which is caused by physical things i.e. sickness). The latter type is the concern of medical doctors in terms of causes and treatment. 

Regarding the spiritual type, professional doctors acknowledge that type, but do nothing about it. However,there are some high-ranking people in the medical profession who are so ignorant and mean that they consider blasphemy a virtue. It is such a people who deny spiritual epilepsy and its effects on the body. This denial is out of pure ignorance. There is nothing in medicine that supports it.

Besides, the practical experience demonstrates the reality of spiritual convulsions. Rational people, who are aware of such spirits and their effects, realize the mental weakness and ignorance of those who deny spiritual epilepsy."

(I say here)

As for the part of the question if the person who was possessed etc is held accountable for that, then usually in the case of someone who was forced into doing something or did something out of forgetfulness etc is absolved from the act and there is no sin upon him as the 'Ulamaa have mentioned in their Fataawa.

Ibn 'Abbaas reported that the Messenger of Allaah said: "Verily Allaah has absolved/pardoned my Ummah for their mistakes, forgetfulness and what they have been forced to do."

And it was reported by Ibn Maajah and Al Bayhaqee and others and it is authentic.

Also, Allaah said in His Book: "...whoever disbelieves in Allaah after his Imaan except the one who was forced but his heart was settled with Imaan..."

Allaah knows best