How to I use Composer to autoload classes from outside the vendor?

The src directory would be in your project root. Its on the same level as vendor directory is.

If you define

"autoload": {
    "psr-4": {
        "DG\Munchkin\": "src/DG/Munch/"
    }
}

this will not load classes from /var/www/html/xxx/vendor/yyy/src/DG/Munch, like you stated.

Because your project structure is:

/var/www/html/
 +- /xxx (project)
     - composer.json
     +- /src
        +- DG
           +- Munch
     +- /vendor
        - autoload.php
        +- vendor-projectA
        +- vendor-projectB
        +- yyy

The DGMunchkin namespace would map to classes inside

/var/www/html/xxx/src/DG/Munch and not inside

/var/www/html/xxx/vendor/yyy/src/DG/Munch.

But how can I load classes from /var/www/html/xxx/?

Define the paths in the composer.json (inside /var/www/html/xxx/) of your project:

"autoload": {
    "psr-4": {
        "ProjectRoot\" : "", 
        "NamspaceInSourceDir\" : "src/"         
    }
 }

or load the composer autoloader in your index.php or during it's bootstrap and add the paths manually:

$loader = require 'vendor/autoload.php';
$loader->add('Namespace\Somewhere\Else\', __DIR__);
$loader->add('Namespace\Somewhere\Else2\', '/var/www/html/xxx');

Referencing: https://getcomposer.org/doc/04-schema.md#autoload

Yes, it is possible, require 'vendor/autoload.php' actually returns an autoloader instance:

/* @var $loader ComposerAutoloadClassLoader */
$loader = require 'vendor/autoload.php';

$class = MonologLogger::class;

$loggerPath = $loader->findFile($class);
if (false === $loggerPath) {
    throw new RuntimeException("Cannot find file for class '$class'");
}
$realLoggerPath = realpath($loggerPath);
if (false === $realLoggerPath) {
    throw new RuntimeException("File '$loggerPath' found for class '$class' does not exists");
}

var_dump($realLoggerPath);

Outputs:

string(64) "/home/user/src/app/vendor/monolog/monolog/src/Monolog/Logger.php"

You should rather take out the implementation details from the war and put in a separate module.

.
├── pom.xml
├── service-api
|   ├── pom.xml
|   └── src
|       └── main
|           └── java
|               └── com
|                   └── 
|                       └── SomeDao.java
├── service-impl
|   ├── pom.xml
|   └── src
|       └── main
|           └── java
|               └── com
|                   └── 
|                       └── SomeDaoImpl.java
└── service-web
    ├── pom.xml
    └── src
        └── main
            └── webapp
                └── WEB-INF
                    └── web.xml

Let service-impl depend on service-api. And service-web will depend on the service-impl.