Did he manage to finish his revenge?
Was all the relationship explained? Cause I read somewhere that his relationship with the princess was kinda left unresolved

His revenge is somehow attained, tho not by the way he depicted. His plan to get the General Albury to be hanged failed, but in the end the general died anyway.
After the dead of the emperor, Orba as the prince went down in one knee and propose to the princess :rolleyes: so idk how in anyway his relation with the princess is unresolved. The princess has stated that she will accept Orba even tho he is a slave, and in unspoken way, both realized that they love each other.
Oh, and the princess asked Orba to spend his life telling her about himself. So I could safely conclude that they marry in near future.
Orba did end up as emperor too. And even tho he spent ten years to finalize it, he finally outlawed slavery.

Orba fake his own death (the prince death, actually) and framed the general Oubary for the deed. This is to accomplish his desire to revenge, and at the same time also get him out of life of being fake prince. Unfortunately, the emperor did not react as he predicted.

The emperor declared that the murder of the prince is the doing of the West. A ploy by Az Bazgan, of whom is in fact someone Orba respected and see as a friend. The princess, knowing this, for the sake of her "late husband" ideas, come to warn Az that Mephius army is marching to subjugate them despite knowing that it will jeopardize her own life. In order to protect the princess, in order to avoid war and unnecessary killing, Orba once more take on the mask of the prince.

Of course, the path back to being crown prince is not that smooth. The emperor outright declared him as imposter, and ordered the nation best generals to bring his head in. Raising the banner of righteousness against the emperor dictactorship, the civil war started. Starting from Apta Fortress, Orba amass his power. More and more, admiration for the "fake prince" grow and Orba managed to conquer half of Mephius before the Emperor gave up and call "the current" Gil Mephius to see him.

The audience session if full of unexpected things and brilliant plot arrangement by the author. Suffice to say that the Emperor know well that the man standing in front of him is a slave, but he is forced to acknowledge him as his son. He recognize that even if he sentenced and exposed Orba, the rebel faction won't be silenced that easily, and will just incite a revolt by saying that the emperor branded his own son with slave mark.

From the princess side, she also somewhat know who Orba really is. The queen Melissa revealed to her that the man who posed as the crown prince is in fact a slave, and she dared the princess to proceed with the wedding, lay with the man and sullied her own noble heritage. This bring the princess to the various interaction she has with Orba the gladiator, and despite the fact that she never see Orba and prince talking, the both of them possess the same insight and Orba seems to know the prince intimately and always been trusted to carry out the most secret mission. After this private revelation, tho it isnt being put into words, we can see that now the princess realize that Orba is the prince, and is fact is fake.

This is also the same time that the princess realize her own feeling, the fact that she has hopelessly fall in love with him. She ended up answering the queen that who that man is, what his life goal, the way of his thinking, she, her own self knows the best, and that is the man she is going to marry. Whether he is the prince or slave isnt important.