What is the ruling on taking part of the cost of device maintenance from customers in advance to guarantee payment, and does this fall under the prohibition of "selling what one does not possess"?

What the questioner mentioned has no relation to the prohibition of selling what one does not own. Rather, it is an advanced portion of the rent, and there is no harm in it, even if it is in the form of a down payment sale (bay' al-'urbun), which means the buyer pays a sum of money to the seller that is counted as part of the price if he takes the item, and belongs to the seller if he leaves it. And leasing (ijarah) is treated the same as selling in this regard.