Magento – What API does the Magento Mobile Store native app use

Magento 1.7 already comes with a REST API. Check system->web services-> REST * admin menu to see if it fits your needs.
Also check this for documentation

You can use the same config generated for the configurable products and used in by the javascript that changes the price based on the selected product options. Here is an example that uses this to determine the minimum and maximum price of a configurable product. The answer is not yet accepted by the OP but I think it works. You can use the same technique, walking through the config array and getting summing up the prices for your values. Don't forget to add the base price at the end. Here is how you can get the config array.

$product = Mage::getModel('catalog/product')->load($productId);
$block = Mage::app()->getLayout()->createBlock('catalog/product_view_type_configurable');
$block->setProduct($product);
$config = json_decode($block->getJsonConfig(), true);
$basePrice = $config['basePrice'];

Looping through $config['attributes'] you can get your desired values.