It is said that there are 10s of reasons as a consequence of which Karna met his death, what are they?
How is he eligible for heaven and liberty, as quoted here?
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There are many reasons For karna's death,as given in Wikipedia
Karna attained Svarga(heaven) not Moksha(liberty) ,as all Kshatriyas(warriors) who die in war are sure to attain heaven.
Lord Krishna says in the Gita that war is like an open door to heaven for a kshatriya
Here is the sloka fore reference:
Yaddrchaya choppapannam svarga dvaaram apavrutam
Sukhinaya Kshatriya Partha labhante yuddham idrsam
The main reasons were
That is the main reason for his death.
He attained paradise, because Indra was bound to take every person to paradise who will die in Mahabharata's Kurukhestra war land.
The Vamana Purana tells how King Kuru came to settle on this land. He chose this land at the banks of Sarasvati River(since dried up before 1900BCE) for embedding spirituality with 8 virtues: austerity (tapas), truth (satya), forgiveness (kshama), kindness (daya), purity (suchee[disambiguation needed]), charity (daan), yagya and brahmacharya. Lord Vishnu was impressed with the act of King Kuru and blessed him. God gave him two boons, one that this land forever will be known as a Holy Land after his name as Kurukshetra (the land of Kuru) and the other that anyone dying on this land will be going to heaven.
Nobody has gone to paradise to see he attained paradise or not, it is written in Mahabharata so we believe he may attained paradise. The point is he was on bad side. And his karma led him to death.