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For example, I have this code:

<p>

"Lorem Ipsum is simply dummy text of the printing and typesetting industry.



Lorem Ipsum has been the industry's standard dummy text ever since the 1500s, when an unknown printer took a galley of type and scrambled it to make a type specimen book.





It has survived not only five centuries, but also the leap into electronic typesetting, remaining essentially unchanged. It was popularised in the 1960s with the release of 



Letraset sheets containing Lorem Ipsum passages, and more recently with desktop publishing software like Aldus PageMaker including versions of Lorem Ipsum."



</p>

Where the correct would be:

<p>Lorem Ipsum is simply dummy text of the printing and typesetting industry.</p>

<p>Lorem Ipsum has been the industry's standard dummy text ever since the 1500s, when an unknown printer took a galley of type and scrambled it to make a type specimen book.</p>

Is it possible to use xpath to do it?
How can I check every p tag, and if the case, format with the correct code?

This code should do what you want. It uses DOMXPath to find all the <p> elements and then splits the content up into separate lines using preg_split, replacing the content of the original <p> element with the first line and then adding new <p> elements as required for each of the subsequent lines.

$doc = new DOMDocument();

$doc->loadHTML($html, LIBXML_HTML_NOIMPLIED | LIBXML_HTML_NODEFDTD);

$xpath = new DOMXpath($doc);

$paras = $xpath->query('//p');

foreach ($paras as $p) {

    $lines = preg_split('/(s*[rn]s*)+/', $p->textContent, -1, PREG_SPLIT_NO_EMPTY);

    $p->textContent = array_shift($lines);

    foreach ($lines as $line) {

        // create a new <p> element

        $new = $doc->createElement('p');

        $new->textContent = $line;

        $p->parentNode->insertBefore($new, $p->nextSibling);

    }

}

echo $doc->saveHTML();

Output for your sample data:

<p>Lorem Ipsum is simply dummy text of the printing and typesetting industry.</p>

<p>Letraset sheets containing Lorem Ipsum passages, and more recently with desktop publishing software like Aldus PageMaker including versions of Lorem Ipsum.</p>

<p>It has survived not only five centuries, but also the leap into electronic typesetting, remaining essentially unchanged. It was popularised in the 1960s with the release of</p>

<p>Lorem Ipsum has been the industry's standard dummy text ever since the 1500s, when an unknown printer took a galley of type and scrambled it to make a type specimen book.</p>

Note that this code will only work when the <p> element does not contain any child HTML elements (e.g. <a> etc.). If that is the case the problem becomes a lot more complex...

Demo on 3v4l.org

I don't think you can do it with Xpath but here php example

<?php

$paragraph = <<<EOF

<p>

"Lorem Ipsum is simply dummy text.



Letraset sheets containing ."



</p>

EOF;



foreach(explode("n", $paragraph) as $line)

{

  if(!empty($line) && strrpos($line, 'p>') === false)

    echo "<p>" . trim($line, '"') . "</p>n";

}

A simple method is to use preg_split() . After that echo them out wrapped in <p> tag

Here are the example

PHP

<?php

// example code



$status = "Lorem Ipsum is simply dummy text of the printing and typesetting industry.



Lorem Ipsum has been the industry's standard dummy text ever since the 1500s, when an unknown printer took a galley of type and scrambled it to make a type specimen book.





It has survived not only five centuries, but also the leap into electronic typesetting, remaining essentially unchanged. It was popularised in the 1960s with the release of 



Letraset sheets containing Lorem Ipsum passages, and more recently with desktop publishing software like Aldus PageMaker including versions of Lorem Ipsum.";





$tagsp = preg_split('/n+/', $status);



foreach($tagsp as $p)

{

    if(strlen($p) > 0)

    {

        echo "<p>$p</p>";

    }

}

DEMO