What are the views of Evangelical Christians on whether it is possible to go to heaven and back to earth? I've heard some stories about how kids have died and come back to life a couple of minutes later with a note or something from heaven (e.g., Colton Burpo). Is this biblical? Is it possible? Could it just be a vision? 

The apostle Paul claims to have gone to the "third heaven," which he also called "Paradise" (2 Corinthians 12:1-4). Is his experience similar to the experiences of other Christians, such as Colton Burpo? 

If, as is likely, there are dissenting views, a complete answer will be an overview presenting brief arguments from both sides.
The devil is in the details, and overall the lame answer is that we just don't have enough details.
But first, addressing your direct questions and examples:

2 Corinthians 12:2-3 ESV I know a man in Christ who fourteen years ago was caught up to the third heaven—whether in the body or out of the body I do not know, God knows. And I know that this man was caught up into paradise—whether in the body or out of the body I do not know, God knows—

Paul says he knows a man (not himself) who was taken up to the third heaven, and that he doesn't know whether it was &quot;in the body or out of the body&quot;--which could easily mean that Paul doesn't know if he literally went to paradise or if it was an out-of-body experience, i.e. a vision. Also, there's no other mention of the third-heaven in scripture, so is Paul talking about heaven or some other paradise? We don't know this either.
And as far as people claiming they went to heaven and back, this is kind of like people claiming they were abducted by aliens: you either take their word for it or you don't. How do they know it wasn't a dream? If they provide &quot;evidence&quot;, how do we know that it's not coincidence? There's not enough tangible evidence one way or the other to know for certain.
I can of only one case in scripture where it a &quot;channel&quot; was opened between heaven and earth: Saul summoning Samuel.

1 Samuel 28:13-15,19 ESV ... Then Samuel said to Saul, “Why have you disturbed me by bringing me up?” Moreover, the Lord will give Israel also with you into the hand of the Philistines, and tomorrow you and your sons shall be with me. The Lord will give the army of Israel also into the hand of the Philistines.

Samuel references the fact that he was &quot;disturbed&quot; and &quot;brought up&quot; and that Saul and his sons would be with him tomorrow, implying that Samuel is indeed in heaven. Samuel does not, however, come back to earth, but simply communicates with Saul.
There's another example of a channel being opened in Jesus' parable of the rich man and Lazarus, but this shows a conversation between residents of heaven and hell, not heaven and earth. This doesn't totally apply to your question, but gives interesting perspective of how God separates the &quot;realms&quot;.

Luke 16:22-26 ESV  The poor man died and was carried by the angels to Abraham's side. The rich man also died and was buried, and in Hades... [Abraham said] 'And besides all this, between us and you a great chasm has been fixed, in order that those who would pass from here to you may not be able, and none may cross from there to us.’

Having said all that, there's no explicit case in scripture of a person literally, physically going to heaven and coming back to earth, only the potential implication noted in 1st Corinthians 12, but even Paul says he doesn't know.
A really good question here would be this: where were Lazarus and Dorcas while they were dead?

John 11:43-44 ESV  When he had said these things, he cried out with a loud voice, “Lazarus, come out.” The man who had died came out, his hands and feet bound with linen strips, and his face wrapped with a cloth. Jesus said to them, “Unbind him, and let him go.”
Acts 9:40 ESV But Peter put them all outside, and knelt down and prayed; and turning to the body he said, “Tabitha, arise.” And she opened her eyes, and when she saw Peter she sat up.

Did they go to heaven? We just don't know. The devil is in the details and there aren't enough details to know for certain that they went to heaven and came back.