Elven power
 

When it says something like "Galadriel was the most powerful elf in Middle earth" what were her powers? Aprart from her ring?

When does it say that? Maybe there talking about her being able to see things through the mirror.

Galadriel's powers mainly lay in the areas of defense and being able to see into others' minds. She learned a lot from Melian the Maia, during her stay in Doriath in the First Age, so the "girdle" around Lothlorien could have been partly derived from the Girdle of Melian around Doriath. She and her people managed to repel three attacks from Dol Guldur, so we know that Lothlorien was a rather strong principality.

Her ability to "use" the Mirror probably lay partly in her mental strength. I believe that it says in The Silmarillion that she was always good at searching the minds of others, but that she never used it to judge them unfairly or harshly.

I can't think of any other "powers" that Galadriel might have.

Well, she was psychic to a degree and telepathic to a degree.

Almost totally telephatic if she wished to be such a thing, a very acurate seer, an healer and the controller of the unnatural weather and time of Lorien.