Did Arjun go to Vaikuntha?

This is not true. Yudhishthira saw Arjuna in the Vaikuntha along with Lord Vishnu. Krishna was in his original Narayana form. He was served by Sudharshana Chakra and other celestial weapons.

Why Krishna showed vishwaroop only to Arjun?

When Krishna gave the teachings of Bhagwad Gita, he showed his Vishwaroop to Arjun to convey him that he is the creator of all humans, operator and also the destructor. Hence, you should not worry about killing your relatives and do your karma. Sanjay also saw this from his divine vision.

Why was Arjuna lucky to see vishvaroopam for the first time?

It also forms the core of Vedanta as it is the part of the prasthana trayi of the Vedanta. Hence gItA is believed to be the greatest of moksha shastra as it focuses on mukti/liberation. As per Geeta none before Arjuna have ever seen the divine Vishvaroopam of Lord Krishna. So Arjuna was the lucky one who witnessed this for the first time ever.

Why didn’t Arjuna practice the given Upadesham?

1. Arjuna did not practice the given upadesham 2. The upadesham was not competent enough (which is unlikely as it was from Lord Krishna himself!). But as per scenario 1. if arjuna did not intend to practice the spiritual discipline then why was he given upadesham at all? if he was not the sadpatra for atma vidya?

Did Arjuna and Yudhishthira go to Hell?

However, as per the mahAbhArata, the pAndavas including Arjuna died in the himAlayas and ascended to hell and heaven respectively. “Yudhishthira, however, was exceedingly disconsolate and stupefied by the foul odour. Resolved to return, O Bharata, he retraced his steps.

Why was Arjun asked to fight in the Battle of Kuruksetra?

Arjun was warrior and his duty was to fight because of his confusion so many doubts and concerns originated in his mind and he started deviating from his true nature. That’s why I think Gita is delivered for people who are searching for answers and Arjun was such a person on that day.