All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.
The procedure of sale that you are asking about has two situations:
Firstly, if the transaction constitutes selling an undefined part of the villa or an undefined period during which each partner has the right to use it, this is allowed. But the rules of buying and selling should be applied. So the buyer becomes a partner in this villa. Hence, he has all the rights of ownership in his owned share and the seller has nothing to do with this sold portion. Then the partners agree between themselves to share the benefit according to their share and each one of them has the full right to do whatever he wants with his owned share, i.e. he can sell it, offer it as a gift, or keep it as a mortgage, etc.
However, when one decides to sell his share, the other partner has the right of Shufa'ah, i.e. purchasing the share of the partner forcefully by giving its price, particularly in immovable properties which are not totally separated. If they are separated then there is no right of Shufa'ah.
Secondly, if the transaction is renting the villa. That's to say, the owner of the villa rents to one person for a period of one month, then to another person for another month, and so on. This is also allowed provided the rulings of renting are met. For example, the period should be specified and it is not allowed to rent it for life, or forever, since the period is not determined and is not known.
As regards combining property sale and rental property, i.e. selling a timeshare for life or forever, not the property itself depriving the purchaser from his right to act freely in the property is not allowed.
As for allotting discount tickets to theme parks to encourage the clients to visit the presentation, this is allowed in principle provided the parks are free from all forbidden activities so that people are not helped in sin and transgression.
With regard to increasing the price against delay in payments this is one of two cases:
Firstly, if this increase is against lending this person the price of the whole villa or part of it, this is forbidden since it is nothing but Ribaa (usury or interest).
Secondly, if the company purchases the villa or part of it and then sells it to the customer with a profit in addition to the amount of purchase in return for the delay in repayments, there is no harm is this and this is what is called Murabaha..
As regards lying to customers to incite them to buy the product, this is forbidden, and it is cheating. The Prophet said: "The seller and the buyer have the right to keep or return goods as long as they have not parted; and if both the parties spoke the truth and described the defects and qualities of the goods, then they would be blessed in their transaction, and if they told lies or hid something, then the blessings of their transaction would be lost" [Al-Bukhari].
The Prophet said: "Whoever cheats is not one of us". [Muslim]
Allaah knows best.