Can a prostitute be classed as "ma malakat aymanakum" (what your right hand possesses) as you through payment she becomes temporarily yours? Please provide clear evidences if possible.
Prostitution is considered haram in Islam. (See IslamWeb for a fatwa on this.)
Sex outside of marriage (zina, or "fornication") is strongly and directly forbidden e.g. in Qur'an 17:32 (...do not approach unlawful sexual intercourse...) and in Sahih al-Bukhari 6810 (...the one who commits an illegal sexual intercourse is not a believer at the time of committing illegal sexual intercourse...).
There's a prescribed hadd punishment when those involved are unmarried (...lash each one of them with a hundred lashes... Qur'an 24:2) and a worse hadd punishment when those involved are married (...stoned to death... Sunan Abi Dawud 4455 [grade: sahih]).
As for using slavery as a mechanism for making fornication halal: Slavery is not considered possible today (Dar Al-Ifta), and previously slavery was restricted to prisoners of war (IslamWeb). See also e.g. Are Muslim men allowed to take “sex slaves?” and Is voluntary slavery Islamic? As such, while in certain circumstances it is halal for a male to have sex with a female slave, one cannot simply "rent" a slave to have sex with them.
Having intercourse with a prostitute is forbidden (even through legal means such as marriage) and makes the person who does it a prostitute as well.
الزاني لا ينكح إلا زانية أو مشركة والزانية لا ينكحها إلا زان أو مشرك وحرم ذلك على المؤمنين
The fornicator does not marry except a [female] fornicator or polytheist, and none marries her except a fornicator or a polytheist, and that has been made unlawful to the believers.
A free person person can not "become" a slave through a contract; enslavement for a price is forbidden:
قال الله ثلاثة أنا خصمهم يوم القيامة ... ورجل باع حرا
Allah says: I will be against three persons on the Day of Resurrection: ... One who sells a free person (as a slave)
Finally, a prostitute isn't your slave, but it is mere words that you say, the evidence is that you do not have real authority over her as you would over a slave. If she is a slave, Can you choose to not free her? Can you take something from her property? Can you choose to not pay her? Can you choose to make her work and give you income? Can you arrange her marriage with someone?
In the name of God, the Most Gracious, Most Merciful
All praise is due to God (ﷻ), the Lord of the Worlds. The Beneficent, the Merciful. Master of the Day of Judgement, and God’s Peace and Blessings be upon Muhammad (ﷺ), his family, his noble Companions, and all those who follow them.
Your question: Is sex with prostitute permissible in Islam?
Answer: Having sex with a prostitute is forbidden because God Said:
"Those who guard their chastity (ie. private parts, from illegal sexual acts) except from their wives or (the captives and slaves) that their right hands possess, - for them, they are free from blame."
— [al-Mu’minoon 23:5-6]
”And compel not your slave-girls to prostitution when they desire to keep chaste, in order to seek the frail goods of this world's life. And whoever compels them, then surely after their compulsion God is Forgiving, Merciful..”
— Quran 24:33
Prostitution (trading sex for money) is haraam. If any does this then he shall be stoned to death. It was practiced by some Arabs during the 6th century. In the 7th century, Muhammad declared that prostitution is forbidden on all grounds.
prophet Muhammad said:
O, you young men! I recommend marriage to you." — The Wasaelush Shia (vol. 14, p. 25)
Do not go near adultery, surely it is an indecency, and an evil way [of fulfilling sexual urge]. (17:32)
So as you can understand from these verses is that once you have sex with a prostitute temporarily then you have committed the sin of Adultery. The best way is, go ahead and marry a woman and finish, problem solved. You won’t need anymore to commit Adultery.
CONCLUSION: You can have sex with a prostitute but you must ask her also if she is agreed for temporary period of time and this must be done after marriage, and not before marriage because it is considered Adultery.