For Sylphiel's relationship with Gourry see the love page.
These two have quite the interesting relationship. To most people it appears as if Sylphiel was created as an obstacle to Lina for Gourry's affection. Most people think that they would fight over the blonde swordsman due to their feelings for him, but the two girls have a deep respect and understanding for one another; showing you can be in love with the same man and still be friends at the same time. Both of the girls though are complete opposites. Lina has a quick temper while Sylphiel on the other hand is very demure. She does argue with Lina but it's mostly for the sake of the world or when she believes Lina is being too hard on Gourry. Lina in turn becomes annoyed at Sylphiel with her unpretentious naivety.
Aside from their mutual feelings for Gourry, they are good influences to each other since they play out the qualities that the other doesn't show very often. Sylphiel helped in her own silent way of making Lina question her feelings for Gourry and Lina does not scold Sylphiel like she would with the others, knowing how fragile she is, especially after Sairaag's destruction. Sometimes she does get on to Sylphiel for a few things but it's mainly her own way to coach her so the shrine maiden will become stronger. It's because of her admiration for Lina that Sylphiel now has more confidence in casting spells that are usually quite difficult for her, since they are not her expertise and together the two make a good team in battle.
At first Zelgadis is a bit cold-hearted and cruel to Sylphiel. He yelled at her when she showed her reluctance towards Lina casting the Giga Slave, and made a harsh comment that other people will die like her father. This was a little bit after Eruk had died so Sylphiel was still in mourning, which made it that much worse. Though Zel could have been more tactful about it, Sylphiel needed that as a wake up call to stop Kopii Rezo before anyone else became hurt. Later on Zelgadis eases up on her and even worries about her safety, which puzzles her -- puzzles us all really. Many support pairing the two together and I admit I could see it a little. Both Sylphiel and Zelgadis are highly introverted and need some peace and quiet to reflect on their lives. Although if Zel really had feelings for Sylphiel I think he wouldn't act so indifferent towards her and be more demonstrative like he was with Miwan who resembles Sylphiel an awful lot.
Amelia doesn't interact as much with Sylphiel as she does with Lina but they look out for each other and are polite and friendly. However, because Amelia is closer to Lina she tends to take the sorceress' feelings into consideration more than Sylphiel's. She distracted Lina from seeing Sylphiel heal Gourry when he was wounded in his fight with Zangulus, but Amelia thought it was something more intimate and didn't want Lina angry. I'm a bit surprised that Amelia isn't closer to Sylphiel though. The girls' past lives are quite similar with both losing their mothers at a young age, raised by their father as the sole parent, and no siblings to grow up with. They're also innocent to the way the world works but while Sylphiel wishes to help those around her, she lacks Amelia's temper and drive.
It's debatable whether or not Sylphiel hated Kopii Rezo. In actuality, anger and hate are foreign emotions to Sylphiel. When Kopii Rezo destroyed half of Sairaag, yes she was naturally upset but Sylphiel didn't show she hated him. After getting over the brief time of grief for her loss she became determined to help in his destruction to prevent anyone else from being hurt. Kopii Rezo might have took pleasure in hearing her screams over her fallen city but he seems to underestimate Sylphiel. He became greatly angry when she interfered in his battle with Lina, but he was also afraid when she discovered the key to destroying him and Zanaffar and used it willingly. I really think that if Sylphiel truly hated Kopii Rezo, then she would have spoken against allowing Flagoon to be his monument.