diff --git a/app/Mage.php b/app/Mage.php
index ec7df4782f2..5a851158a5b 100644
--- a/app/Mage.php
+++ b/app/Mage.php
@@ -14,8 +14,9 @@
  * @license    https://opensource.org/licenses/osl-3.0.php  Open Software License (OSL 3.0)
  */
 
-define('DS', DIRECTORY_SEPARATOR);
-define('PS', PATH_SEPARATOR);
+defined('DS') || define('DS', DIRECTORY_SEPARATOR);
+defined('PS') || define('PS', PATH_SEPARATOR);
+
 define('BP', dirname(__DIR__));
 
 Mage::register('original_include_path', get_include_path());
@@ -278,7 +279,7 @@ public static function register($key, $value, $graceful = false)
             if ($graceful) {
                 return;
             }
-            self::throwException('Mage registry key "' . $key . '" already exists');
+            self::throwException("Mage registry key $key already exists");
         }
         self::$_registry[$key] = $value;
     }
@@ -331,7 +332,7 @@ public static function setRoot($appRoot = '')
         if (is_dir($appRoot) && is_readable($appRoot)) {
             self::$_appRoot = $appRoot;
         } else {
-            self::throwException($appRoot . ' is not a directory or not readable by this user');
+            self::throwException("$appRoot is not a directory or not readable by this user");
         }
     }
 
@@ -493,14 +494,18 @@ public static function getConfig()
      * @param callback $callback
      * @param array $data
      * @param string $observerName
-     * @param string $observerClass
+     * @param class-string|'' $observerClass
      * @return Varien_Event_Collection
+     * @throws Mage_Core_Exception
      */
     public static function addObserver($eventName, $callback, $data = [], $observerName = '', $observerClass = '')
     {
         if ($observerClass == '') {
             $observerClass = 'Varien_Event_Observer';
         }
+        if (!class_exists($observerClass)) {
+            self::throwException("Invalid observer class: $observerClass");
+        }
         $observer = new $observerClass();
         $observer->setName($observerName)->addData($data)->setEventName($eventName)->setCallback($callback);
         return self::getEvents()->addObserver($observer);
@@ -638,14 +643,17 @@ public static function getResourceHelper($moduleName)
     /**
      * Return new exception by module to be thrown
      *
-     * @param string $module
+     * @param string $moduleName
      * @param string $message
-     * @param integer $code
+     * @param int $code
      * @return Mage_Core_Exception
      */
-    public static function exception($module = 'Mage_Core', $message = '', $code = 0)
+    public static function exception($moduleName = 'Mage_Core', $message = '', $code = 0)
     {
-        $className = $module . '_Exception';
+        $className = $moduleName . '_Exception';
+        if (!class_exists($className)) {
+            $className = 'Mage_Core_Exception';
+        }
         return new $className($message, $code);
     }
 
@@ -654,6 +662,7 @@ public static function exception($module = 'Mage_Core', $message = '', $code = 0
      *
      * @param string $message
      * @param string $messageStorage
+     * @return never
      * @throws Mage_Core_Exception
      */
     public static function throwException($message, $messageStorage = null)
@@ -784,8 +793,8 @@ public static function run($code = '', $type = 'store', $options = [])
      */
     private static function _setIsInstalled($options = [])
     {
-        if (isset($options['is_installed']) && $options['is_installed']) {
-            self::$_isInstalled = true;
+        if (isset($options['is_installed'])) {
+            self::$_isInstalled = (bool) $options['is_installed'];
         }
     }
 
diff --git a/app/code/core/Mage/Core/Model/Config.php b/app/code/core/Mage/Core/Model/Config.php
index f88d34aa119..12f58250faa 100644
--- a/app/code/core/Mage/Core/Model/Config.php
+++ b/app/code/core/Mage/Core/Model/Config.php
@@ -1333,17 +1333,17 @@ public function getPathVars($args = null)
      * Retrieve class name by class group
      *
      * @param   string $groupType currently supported model, block, helper
-     * @param   string $classId slash separated class identifier, ex. group/class
+     * @param   string $classAlias slash separated class identifier, ex. group/class
      * @param   string $groupRootNode optional config path for group config
      * @return  string
      */
-    public function getGroupedClassName($groupType, $classId, $groupRootNode = null)
+    public function getGroupedClassName($groupType, $classAlias, $groupRootNode = null)
     {
         if (empty($groupRootNode)) {
             $groupRootNode = 'global/' . $groupType . 's';
         }
 
-        $classArr = explode('/', trim($classId));
+        $classArr = explode('/', trim($classAlias));
         $group = $classArr[0];
         $class = !empty($classArr[1]) ? $classArr[1] : null;
 
@@ -1395,8 +1395,8 @@ public function getGroupedClassName($groupType, $classId, $groupRootNode = null)
     /**
      * Retrieve block class name
      *
-     * @param   string $blockType
-     * @return  string
+     * @param string $blockType
+     * @return string
      */
     public function getBlockClassName($blockType)
     {
@@ -1409,15 +1409,15 @@ public function getBlockClassName($blockType)
     /**
      * Retrieve helper class name
      *
-     * @param   string $helperName
+     * @param   string $helperAlias
      * @return  string
      */
-    public function getHelperClassName($helperName)
+    public function getHelperClassName($helperAlias)
     {
-        if (!str_contains($helperName, '/')) {
-            $helperName .= '/data';
+        if (!str_contains($helperAlias, '/')) {
+            $helperAlias .= '/data';
         }
-        return $this->getGroupedClassName('helper', $helperName);
+        return $this->getGroupedClassName('helper', $helperAlias);
     }
 
     /**
@@ -1445,8 +1445,8 @@ public function getResourceHelper($moduleName)
     /**
      * Retrieve module class name
      *
-     * @param   string $modelClass
-     * @return  string
+     * @param string $modelClass
+     * @return string
      */
     public function getModelClassName($modelClass)
     {
diff --git a/app/code/core/Mage/Core/Model/Layout.php b/app/code/core/Mage/Core/Model/Layout.php
index 576c5a32476..eea3b34c56d 100644
--- a/app/code/core/Mage/Core/Model/Layout.php
+++ b/app/code/core/Mage/Core/Model/Layout.php
@@ -595,12 +595,13 @@ public function getMessagesBlock()
     /**
      * @param string $type
      * @return Mage_Core_Block_Abstract|object
+     * @throws Mage_Core_Exception
      */
     public function getBlockSingleton($type)
     {
         if (!isset($this->_helpers[$type])) {
             $className = Mage::getConfig()->getBlockClassName($type);
-            if (!$className) {
+            if (!$className || !class_exists($className)) {
                 Mage::throwException(Mage::helper('core')->__('Invalid block type: %s', $type));
             }