When a customer creates a shopping cart (adds an item to the cart) an ItemPricingEngine loads item-level promotions for that particular customer
when ItemPricingEngine calls while adding item to cart(in which class)
ItemPrcingEngine will be called while doing the "repriceOrder" after adding an item to cart.Below is the OOTB flow for adding an item to cart
From PurchaseProcessHelper's addItemsToOrder() method repriceOrder chain will be called from the method "runProcessRepriceOrder".
In "repriceOrder" commercePipeline ItemPricingEngine will be called.
You may not be able to see what exactly you are looking for as ATG has proprietary code. But just like other modules like DAS, DPS etc. some of the commerce module code is also provided for reference. You can look into the <ATG>\DCS\src\Java to explore and refer the code that has been provided. E.g. repriceOrder commerce pipeline chain has its PipelineProcessor object specified as atg.commerce.pricing.processor.PriceOrderTotal whose source is available in <ATG>\DCS\src\Java.