So i know roman slaves were very expensive and because of that treated well, often like a member of family, as well as freed and even married as free people by their owners. I know they were treated like a property though, considering that, could a roman slave have a romantic relationship? As in date a woman, maybe other slave or a free peasant that also works on his owners land? Or would this not be possible?
Well, as far as a slave can give consent, yes.
Apuleius in his 2nd C CE novel describes a relationship between a traveler and the slave girl for the house in which he was staying, where she was sneaking around to sex him, until he got turned into a donkey.
Cato the elder had a relationship with a slave after his wife died, but his son objected to it and he cut that off IIRC.
I'm don't know what else could be added. We have a fictional romantic relationship with a slave and a real romantic relationship with a slave.
I'll give Plutarch's version of the Cato-Slave story, I guess.
After the death of his wife, he married his son to the daughter of Aemilius Paulus, the sister of Scipio, but he himself, in his widowhood, took solace with a slave girl who secretly visited his bed. Of course, in a small house with a married woman in it, the matter was discovered, and once, when the girl seemed to flaunt her way rather too boldly to the chamber, the old man could not help noticing that his son, although he said nothing, looked very sour, and turned away. Perceiving that the thing displeased his children, Cato did not upbraid or blame them at all, but as he was going down in his usual way to the forum with his clients, called out with a loud voice to a certain Salonius, who had been one of his under-secretaries, and was now in his train, asking him if he had found a good husband for his young daughter. The man said he had not, and would not do so without first consulting his patron. "Well then," said Cato, "I have found a suitable son-in‑law for you, unless indeed his age should be displeasing; in other ways no fault can be found with him, but he is a very old man." Salonius at once bade him take the matter in charge and give the maid to the man of his choice, since she was a dependant of his and in need of his kind services. Then Cato, without any more ado, said that he asked the damsel to wife for himself. At first, as was natural, the proposal amazed the man, who counted Cato far past marriage, and himself far beneath alliance with a house of consular dignity and triumphal honours; but when he saw that Cato was in earnest, he gladly accepted his proposal, and as soon as they reached the forum the banns were published.