All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
May Allah reward you greatly for keenly seeking after what is lawful and asking about the Sharee‘ah ruling before entering into any transaction; this is becoming of a Muslim who is keen to maintain his religiosity and obtain lawful earnings.
As for your questions, we will sum up the answer to them in the following points:
First: giving fake reviews of a product to lure people into buying it or the like is impermissible. The Lawgiver has forbidden deceiving a buyer in similar manners, for example by expressing one’s desire to buy a commodity, highlighting its good quality, and that it is worth more than its value in order to tempt the potential buyer to buy it. Therefore, it is incumbent to refrain from giving such fake reviews of products because it falls into the category of prohibited cheating and deception, even if it is done free of charge. Whatever compensation one may be receiving in return for it is unlawful and evil earning.
Second: deceiving the website by making a product seem appealing (to customers) and a “big seller” to rank on its first pages, while it is actually not and you are, in fact, arranging with people to buy it, and they actually buy it and then you give them a refund, is also prohibited because it involves cheating and deception. It was narrated that the Prophet, sallallaahu ‘alayhi wa sallam, said: “Whoever cheats is not one of us.” [Muslim] The version cited by At-Tabaraani has the addition: “....and fraud and deceit are in Hellfire (i.e. lead to it).”
You may promote the product by means of legitimate incentives, such as offering discounts or giving gifts, whose nature is known, to the buyers, and the like. Thus, you can fulfill your objective in a way that does not involve cheating or deceit.
Third: as for deleting the negative comments, if the website authorizes this, then there is nothing wrong with it. However, if the product is defective, the defect must be made clear to the buyer. Honesty begets blessing, while lying deprives the sale of all blessing. It was authentically reported that the Prophet said: “…and if both parties speak the truth and describe the defects and qualities of the goods (honestly), their transaction will be blessed for them, but if they tell lies or hide the defects, there will be no blessing in their sale transaction.”
We ask Allah, The Exalted, to suffice us with what is lawful against what is unlawful, and to apportion for us a share of fear of Him that deters us from disobeying Him.
For more benefit on listing and selling products on Amazon, please refer to Fataawa 351583 and 352363.
Allah Knows best.