I'm sorry that you don't like the definition I posted, but word means things, and self-willed means in every major dictionary I can find, some variant of headstrong (Oxford, Cambridge) obstinate (merriam-webster), stubborn (Collins)... no, the idea that it doesn't mean those thing os not reasonable.
I have quoted the passage that includes the line about pursuing Feanor to the end of the earth in my previous post. You responded to it with "Galadriel is awesome", I believe. The key passage is this:
"but now she burned with desire to follow Feanor with her anger to whatever land he might come, and to thwart him in all ways that she could." I already coted the source, but it"s from People of Middle Earth, the Shibboleth of Feanor.
On the dragon thing, well, I could point out that sword-wielding being a commonplace activity in Middle Earth comparing it to dragon shifting is ridiculous, buuuuuttt this is much funnier:
Galadriel's brother, Finrod, shapeshifted himself and Beren into orcs. That's canon.
Galadriel's first cousin once removed, Luthien, shapeshifed herself into a (flying) vampire and Beren into a very large werewolf. That's canon,
Galadriel hersel appears to change her size during that whole incident with thr Ring, although that could be the Ring playing on Frodo's mind.
...yeah, I would 't make any large bet about what Galadriel can or cannot shapeshift into,