If I am writing a paper about Heaven, do I capitalize Heaven or keep it like heaven.?

Heaven is a proper noun, just like Hogwarts or Narnia.

Depends on the use. If you're using the original meaning, it's "the heavens", which refers to the sky, basically. So lowercase there. If you're using it to refer to the ethereal realm where the Christian god is supposed to dwell, it's a proper name, so it's capitalized: Heaven.

It is a name of a place, right? These need to be capitalized in English.

Heaven is a proper noun

Proper nouns are capitalized.

It's a proper noun.

It is a specific place, like California or Venus or Utopia, so it is capitalized.

heaven doesn't exist

heaven as it isn't a real thing

Lower case is best, because the Christian afterlife concept is just as delusional as the after life concept of any other faith.