Is there a bad part of heaven?

Question

From what I understand, by Catholics, everyone who believes in Jesus goes to Heaven, but most people go to purgatory first. When they leave purgatory, everyone is worthy of some level of Heaven. Everyone who does not believe in Jesus goes to Hell and there is a pretty nice section at the top of Hell for righteous heathens.

Protestants tend not to believe in Purgatory. There is only Heaven and Hell. It seems to me that you can get people who are really rotten but, since they believe all the requisite things, go to Heaven.

1) Do we say that if they had REALLY believed in Jesus they wouldn't have been bad and these people are actually in Hell?

OR

2) Is there a "bad" part of heaven for these souls?

If so, is this bad part good, but not as nice as the other parts of heaven and the soul experiences some torment knowing they are in the bad section

Is this bad place actively bad, but not as bad as Hell (sort of like a prison on the outskirts of heaven?)

I am interested in the types of Protestantism that flourish in America.

Related, but does not address the hell issue:

Are all humans in Heaven equal or is there also a kind of hierarchy? (Roman Catholic perspective)

Answer 1

It seems to me that you can get people who are really rotten but, since they believe all the requisite things, go to Heaven.

Yep, although it's not really about intellectual belief/assent, but that the person trusts God to fulfil all his promises and lives as though they do trust God, i.e., repentance.

These really rotten people are in fact every single human person. As Romans 3:10-18 says:

“There is no one righteous, not even one;
  there is no one who understands;
  there is no one who seeks God.
All have turned away,
  they have together become worthless;
there is no one who does good,
  not even one.”
“Their throats are open graves;
  their tongues practice deceit.”
“The poison of vipers is on their lips.”
  “Their mouths are full of cursing and bitterness.”
“Their feet are swift to shed blood;
  ruin and misery mark their ways,
and the way of peace they do not know.”
  “There is no fear of God before their eyes.”

Every single person in heaven/on the new earth after resurrection is an evil, sinful, rotten human being who deserves God's wrath and destruction.

Many, probably most, Protestants recognise that several Bible passages seem to indicate that there will be different levels of reward in the afterlife. So although we can never merit acceptance by God, the good that we do will be recognised. This page by J. Warner Wallace seems like a good summary of these passages.

To paraphrase the KJV of John 14:2-3, Jesus is preparing mansions for all his people, and no one deserves a mansion, but some people's mansions will be bigger than other people's mansions. But freed from the sin of envy, when we meet someone on the new earth with a bigger mansion than our own all we will do is praise God that he was working in someone's life to a greater degree than our own!