Hello
As per your description understood the requirement complete.
You are looking for an API or such code through which you can connect your loud based ERP system which your online shot so that you can manage orders and inventory as well.
We can develop such API. I would like to tell that we have expertise in Prestashop and can easily work on this project. I did see your project requirement and really very interested because we are working and expert in: Designing, HTML5, CSS3, BOOTSTRAP, JQUERY, JAVASCRIPT, AJAX
PHP, MYSQL, CMS(Word Press, JOOMLA, Drupal) Magento, CRM, .Net framework, SQL Server, Android and IOS Development.
Framwork: CakePHP, Zend, CI.
Please initiate a chat so I can explain my expertise.
Looking forward for your reply
Thanks