His teacher (Minato) was under Jiraiya's supervision, and Jiraiya and Orochimaru were teammates. There is no relationship at all. They would be linked if Orochimaru's partner, Jiraiya, trained Minato, who in turn trained Kakashi. This partnership ended when Jiraiya died.
Orochimaru also had relationships with other ninja of the village. He even married one called Susanoojime, but she was actually an immortal named Shekhinah.
As for liking someone, I don't think so. He used to kill his students but then again he was a demon so maybe not.
She didn't do it. Tsunade once informed Jiraiya that if she had to pick between him and Orochimaru for a boyfriend, she would surely choose Orochimaru. That didn't necessarily imply she was interested in him romantically. She could have been making an effort to protect his feelings.
Also, note that when Tsunade first meets Naruto, she calls him "my boy". This could be taken as a sign of affection towards him.
Tsunade is shown to have a strong sense of justice, which makes her unlikely to have any romantic feelings towards someone like Orochimaru. She also seems to dislike the fact that he used her in his experiments, which would make her unwilling to show him any kind of favor too.
Now, regarding her comment about choosing between them: It's possible that she was just being polite and not wanting to offend either man by saying something that might cause one of them to leave. She probably wouldn't say this kind of thing normally so we can assume it was just before entering into a very important conversation.
Orochimaru was probably aware of this comment and took advantage of it by asking Jiraiya to send him Naruto so he could experiment on him. Tsunade being the kind-hearted woman that she is agreed to let him do so.
Orochimaru was an orphan who studied under Hiruzen Sarutobi with Jiraiya and Tsunade. In comparison to the more laid-back Jiraiya, Orochimaru stood out as a genius—Hiruzen judged his abilities, knowledge, and resolve to be those of a prodigy seen once in a generation. However, while Jiraiya enjoyed traveling around Konoha, fighting evil, and having fun, Orochimaru used his intelligence to create weapons and technology that would make him seem like a demon to others.
As time passed, Orochimaru gained power over both Heaven and Earth, until he declared himself "the true king of the ninja". At this point, Jiraiya left to train under another sensei and never returned. All that remains of him are two scrolls containing techniques that only he knew how to use.
Tsunade also left home when she was young. She grew up under the care of her father, who was obsessed with creating powerful ninja. When she became old enough, she decided to leave too, but not before teaching Orochimaru her medical skills so he could fight along side her as a surgeon.
Orochimaru has no real family or friends other than his many slaves who will do anything for his favor. He is cold, ruthless, and will stop at nothing to get what he wants.
Jiraiya began to track Orochimaru's movements as well as those of Akatsuki, a group that Orochimaru later joined. His investigations frequently kept him away from the village, preventing Jiraiya from becoming the Fifth Hokage, as Hiruzen desired. However, when Nagato sought out Jiraiya to recruit him to Akatsuki, Jiraiya followed him out of respect for his former student.
During the Warring States period, Jiraiya traveled extensively throughout Japan looking for powerful enemies that he could defeat in order-upcoming events. He eventually met up with Orochimaru in one such town and agreed to travel with him to Akatsuki. There, Jiraiya was given a choice by Nagato: join him or be killed. Reluctant at first, Jiraiya eventually joined forces with Akatsuki and began to learn how to summon demons.
In time, it became clear that Nagato was using Jiraiya as a pawn in his plans against Konohagakure. When Nagato was about to destroy it with its own jinchūriki, however, he discovered that Jiraiya was not yet loyal to him. Realizing that he needed to show Jiraiya love in order to win his trust, Nagato sent his snake puppets to kill him.
Orochimaru was expelled from Konoha, and while there, he rejected down the position of Hokage. He was adamantly opposed to taking on the duty. Jiraiya even stated that when his parents died, Orochimaru transformed and attempted to study jutsus that would bring his parents back to life. When this failed, he abandoned his studies and traveled the world in order to find a way to revive them.
During one of his travels, Orochimaru met with a member of another ninja clan who had found a way to revive their dead by using bloodlines. This clan was called "The Uchiha". The two began working together to create many new vampires. When they were done, Orochimaru brought these vampires back to Konoha where they were given human bodies. The only thing is that these vampires needed feeding on blood to survive so Orochimaru ordered some of his minions to go around killing people for their blood.
When this became too easy, Orochimaru decided to make things more interesting by turning some of the humans against their own clans using his favorite technique: Love. This caused many fights to break out between the vampires and their former teammates which led to Konohagakure's decision to expel him. After this incident, Orochimaru left Konoha and hasn't been seen or heard from since.
Some sources say that it was because of all of the deaths he caused by creating vampires but this isn't clear cut.
He attempts to earn the love and admiration of the lovely Tsunade, who employs slug magic. According to the original narrative, Orochimaru was Jiraiya's student. He was known as Yashagoro, but he was gradually corrupted by evil magic. He became Orochimaru, the serpent master, and his old master's sworn nemesis. In the final episode of the series, it is revealed that Tsunade is actually Orochimaru's daughter.
Orochimaru likes beautiful things such as flowers and music. He also likes powerful techniques such as Amaterasu and Susanoo.
In addition to using his own body as a weapon, Orochimaru has been known to use weapons made of bone or ice. He has been seen using fireballs, lightning bolts, and even giant snakes. He has also been known to borrow other people's powers during battle. For example, when Jiraiya was killed by Tobi, it was Orochimaru who took over and attacked Nagato. During this time, he used his own eye sockets as wells for Jiraiya's elemental powers so he could fight better.
Orochimaru has also been known to use animals as weapons or allies. For example, he has used snake tails as shurikens, rats as spy devices, and birds as messenger boys.
When not fighting evil, Orochimaru likes to play music on his koto.