Thank you for this bug report. To properly diagnose the problem, we
need a short but complete example script to be able to reproduce
this bug ourselves. 

A proper reproducing script starts with <?php and ends with ?>,
is max. 10-20 lines long and does not require any external 
resources such as databases, etc. If the script requires a 
database to demonstrate the issue, please make sure it creates 
all necessary tables, stored procedures etc.

Please avoid embedding huge scripts into the report.

What you have there is complicated and incomplete. I tried a brief test script that includes closures, references, and the constructor as are used in your class but I get the expected behavior.

<?php
abstract class Base{
  protected $funcs = [];

	public function __call($name, $args) {
		error_log("\t>>>Call [$name](". json_encode($args). ") \r\n",3, LOGFILE);

		if (method_exists($this, $name)) {
			return call_user_func_array($this->$name, $args);
		} else if (isset($this->funcs[ $name ])) {
			return call_user_func_array($this->funcs[ $name ], $args);
		} else {
			throw new Exception("Method <$name> is not accessible.");
		}
	}

	/**
	 * @param array $args
	 *
	 * @example   new Base(["field1"=>"value1", "field2"=>"value2"])
	 *            if u need override __constructor, then use:
	 *            __construct($args){
	 *            ..
	 *            parent::__construct($args);
	 *            }
	 */
	public function __construct($args = []) {
		$nameClass = get_class($this);

		#region auto create methods 'hasField' for everyone field\property (if there exists getter or setter)
		$properties = get_class_vars($nameClass);
		$keys = array_keys($properties);
		foreach ($keys AS $k) {
			if ((method_exists($this, "set" . ucfirst($k)) || method_exists($this, "get" . ucfirst($k)))
					&& (!method_exists($this, "has" . ucfirst($k) && !isset($this->funcs["has" . ucfirst($k)])))
			) {
				$v = &$this->$k;
				$this->funcs["has" . ucfirst($k)] = function () use (&$v) { return !empty($v); };
			}
		}
		#endregion

		foreach ($args as $k => $v) {
			if (property_exists($nameClass, $k)) {
				$this->$k = $v;
			}
		}
	}
}

class Test extends Base{
  private $field1;
  public function setField1($v){$this->field1 = $v;}
  public function getField1(){return $this->field1;}

}

$test = new Test();
$test->setField1(23423);
echo $test->hasField1();
?>

get_class_vars() will not show you private variables unless you call it from within their defining class. While you could call it from within the child in abstract "helper" method, the parent would still not have access to the variable and would thus error.
On the other hand, protected variables *are* accessible from parents so you could make the variable protected and the code would work.

But what about question 2)?
I see only hasField1 call

As do I. hasField1 is the only method that does not exist/is not accessible, and it is only called once. What's the problem?

I was expecting at least the message of two calls: setField1 and hasField1.
why there is no information about the call setField1?

http://php.net/manual/en/language.oop5.overloading.php#object.call
>__call() is triggered when invoking inaccessible methods in an object context.

oh, thanks. I'm sorry
I have no more questions