Is the described commercial transaction, which involves setting the price and providing goods for a known term, paying part of the price in advance upon acceptance, and then paying the remaining part after delivering the goods and receiving the rest of the price from the buyer, legitimate? And what is the legitimate method for such transactions if it is not?

A supply contract is an agreement to deliver specific goods periodically over a certain period for a fixed sum. If the goods require manufacturing, the contract is one of istisna' (manufacturing contract). If they do not require manufacturing and are described in terms of their characteristics, the contract is a salam (forward sale) contract, provided the price is paid in full upfront. If the price is not paid in full upfront, it is not permissible unless the promise is non-binding. This pitfall can be avoided by making the agreement a non-binding promise, or by making the supplier an agent for the importer.