All the answers for these questions can be found in Sabha parva and Swargarohana parva.
Why Duryodhana attained heaven?
Duryodhana attained heaven due to his practice of Kshatriya dharma on the battlefield.
Sage Narada mentions this to Dharma raja as part of their conversation in heaven
"Narada, smiling, told him, ‘It should not be so, O king of kings. While residing in Heaven, all enmities cease. O mighty-armed Yudhishthira, do not say so about king Duryodhana. Hear my words. Here is king Duryodhana. He is worshipped with the gods by those righteous men and those foremost of kings who are now denizens of Heaven. By causing his body to be poured as a libation on the fire of battle, he has obtained the end that consists in attainment of the region for heroes. You and your brothers, who were veritable gods on Earth, were always persecuted by this one. Yet through his observance of Kshatriya practices he has attained to this region. This lord of Earth was not terrified in a situation fraught with terror.
I personally don't think he was a villain?
Sage Narada enlisted the mistakes done by Duryodhana and why Dharma raja should forgive him in the following conversation in heaven
"‘O son, thou shouldst not bear in mind the woes inflicted on thee on account of the match at dice. It behoveth thee not to remember the afflictions of Draupadi. It behoveth thee not to remember the other woes which were yours in consequence of the acts of your kinsmen,—the woes, viz., that were due to battle or to other situations. Do thou meet Duryodhana now according to the ordinances of polite intercourse. This is Heaven, O lord of men. There can be no enmities here.’
Defeating another king using magical dice. Asking wife of your brother who is equivalent to your mother to be brought into the sabha. Not returning the kingdom back to his brothers once they held their end of bargain. Trying to kill them using wax house and lighting it. I think after enlisting all these things there would be no one saying he is not a villain.
Draupadi was not molested?
First we need to understand that Matha Draupadi is never lost in dice game. The following question by her goes unanswered because she has asked the right question and there is no right for any one to put his wife as stake once he lost himself first.
"Draupadi said,--'O son of the Suta race, go, and ask that gambler present in the assembly, whom he hath lost first, himself, or me. Ascertaining this, come hither, and then take me with thee, O son of the Suta race.'
So technically Dharma raja did so only on insistence of Shakuni who is playing on behalf of Duryodhana who has become the master of Dharma raja due to previous bet. Respecting the wish of master is another part of Dharma and Dharma raja obliged with that.
So there is no right for anyone to bring Draupadi devi to sabha and they did so against her wishes which attributes to molestation. There is no evidence say anything contrary to this and it is blatant case of molestation without any doubt.
Will Duryodhana stay in heaven forever?
The following words of Indra will give an insight of what will happen next to people who commit a lot of sins
‘O Yudhishthira of mighty arms, come, come, O chief of men. These illusions have ended, O puissant one. Success has been attained by thee, O mighty-armed one, and eternal regions (of felicity) have become thine. Thou shouldst not yield to wrath. Listen to these words of mine. Hell, O son, should without doubt be beheld by every king. Of both good and bad there is abundance, O chief of men. He who enjoys first the fruits of his good acts must afterwards endure Hell. He, on the other hand, who first endures Hell, must afterwards enjoy Heaven. He whose sinful acts are many enjoys Heaven first. It is for this, O king, that desirous of doing thee good, I caused thee to be sent for having a view of Hell. Thou hadst, by a pretence, deceived Drona in the matter of his son. Thou hast, in consequence thereof, been shown Hell by an act of deception. After the manner of thyself, Bhima and Arjuna, and Draupadi, have all been shown the place of sinners by an act of deception. Come, O chief of men, all of them have been cleansed of their sins. All those kings who had aided thee and who have been slain in battle, have all attained to Heaven. Come and behold them, O foremost one of Bharata’s race.
So there is definitely going to be hell for mistakes done and it will be delivered once all the result of good acts is complete.