Hello!
If you want to use the API of the Storefront REST API add-on, make sure that you make requests to its endpoints in the correct way. Like http://example.com/api/4.0/sra_products for the \Tygh\Api\Entities\v40\SraProducts (app/addons/storefront_rest_api/Tygh/Api/Entities/v40/SraProducts.php)
As for the way to place orders, take a look at the Orders API entity:
https://docs.cs-cart.com/latest/developer_guide/api/entities/orders.html
For the shopping cart entity, have a look at the \Tygh\Api\Entities\v40\SraCartContent entity. And for payments, have a look at the \Tygh\Api\Entities\v40\SraSettlements entity. I am afraid there is no documentation for the entities from this add-on, so you will have to examine their code in order to make the correct request.