السلام عليكم ورحمة الله وبركاته Ustadh, may a closer close a deal if: 1) a third party like Klarna pays the company upfront and the customer repays monthly, and 2) the customer pays in installments but is charged interest for late payment?

All of this depends on your involvement. The first one is allowed if the company purchases the item, then afterwards it makes the contract with the buyer to buy from them on installments, even if they increase the price, as long as they do not put late fees or other forbidden things. The second one, if you do not aid in the riba involved then there is nothing on you and you can close, otherwise it is riba.