I would say this is the The Hourglass Door from the Hourglass Door Trilogy by Lisa Mangum.
Description from Amazon
Abby[']s senior year of high school is textbook perfect: She has a handsome and attentive boyfriend, good friends, good grades, and plans to attend college next year. But when she meets Dante Alexander, a foreign-exchange student from Italy, her life suddenly takes a different turn. He[']s mysterious, and interesting, and unlike anyone she[']s ever met before. Abby can[']t deny the growing attraction she feels for him. Nor can she deny the unusual things that seem to happen when Dante is around. Time behaves differently when they are together traveling too fast or too slow or sometimes seeming to stop altogether. When the band Zero Hour performs at the local hangout, Abby realizes that there[']s something dangerous about the lead singer, Zo, and his band mates, Tony and V. Oddly, the three of them are also from Italy and have a strange relationship to Dante. They also hold a bizarre influence over their audience when performing. And Abby[']s best friend, Valerie, is caught in their snare. Dante tells Abby the truth of his past: he once worked for Leonardo Da Vinci, helping to design and build a time machine. When Dante was falsely implicated as a traitor to his country, he was sent through the machine more than five hundred years into the future as punishment. As the past and the present collide, Abby learns that she holds a special power over the flow of time itself. She and Dante must stop Zo from opening the time machine[']s door and endangering everyone[']s future. More than one life is at stake and Abby[']s choice could change everything.
It seems to include all the elements you talked about, a group that is timeless (doesn't age), time manipulation, and one of them falling for a girl, and a female author.