Hello,
I provided the link to the pre-sale questions because I feel that this should not be discussed here, as WooCommerce Multilingual is a free add-on that bridges WPML and WooCommerce, and this forum is focused on WooCommerce Multilingual.
About the Laravel app that you have – if you can modify the request that is sent by that application to include the required parameters that I mentioned above – then you should not have issues.
If you require support related to the functionality that we provide, you can ask for that here (but here we cannot get access details to your site, so we are a bit limited), or in our forum at WPML.org(where we can activate private reply, or you can provide credentials for access and debugging right when you create a ticket)
Speaking strictly about REST requests in WooCommerce Multilingual, we can help you if you have problems with them. So, yes, WPML provides support for WooCommerce Multilingual.
However, if a REST request is working, but your Laravel app is not – then you should contact your Laravel app developer and provide him with the information from my previous reply on how to modify the REST request so that it works, and we cannot provide support for that.
I hope that I have explained it more clearly now.