"to be happy" is translated as "бути щасливим". "Мені весело зараз" is better to translate as "I have fun now". "to be happy" and "to have fun" is not the same!
Where did "feel" come from? If it is implied, then why did DL not use it in the prior example: "Мені самотньо зараз." which DL translated as "I am lonely now." and not "I feel lonely now."
I tested and "I feel lonely now." is marked as incorrect.
These are 2 different ways of saying “be happy”-бути щасливим. Like in English - to be is used for conveying state，so “Я щасливий або Я старий”. Feel is used in the same way， but usually only for conveying temporary feelings - “Я сумний” - I am sad. It should have accepted your answer.