How can I update code that uses the deprecated each() function?

For your first two example cases, you could use key() and current() to assign the values you need.

$ar = $o->me;   // reset isn't necessary, since you just created the array
$typ = key($ar);
$val = current($ar);

$out = array('me' => array(), 'mytype' => 2, '_php_class' => null);
$expected = [key($out), current($out)];

In those cases, you can use next() to advance the cursor afterward, but it may not be necessary if the rest of your code doesn’t depend on that.

For the third case, I’d suggest just using a foreach() loop instead and assigning $kv inside the loop.

foreach ($broken as $k => $v) {
     $kv = [$k, $v];
}

For the fourth case, it looks like the key is disregarded in list(), so you can assign the current value.

$this->result = current($this->cache_data);

Like the first two cases, it may be necessary to advance the cursor with next() depending on how the rest of your code interacts with $this->cache_data.

Fifth can be replaced with a for() loop.

reset($array);
for ($i = 0; $i < 30; $i++) {
    $id = key($array);
    $item = current($array);
    // code
    next($array);
}