Legolas' name is not 'Legolas Greenleaf', and he would never introduce himself as such. 'Greenleaf' is what his name means in Elvish. If you must give him a surname, use 'Thranduilion', which means 'son of Thranduil'. That's probably how he would have been referred to anyway.
The plotline seems to be jumping around a little bit. The argument between Legolas and Boromir was very OOC, and I don't see why so far all the males seem attracted to Solaris.
Why is it suddenly Aragorn and Arwen again? Unless I'm much mistaken, in the previous chapter you had Thranduil saying something about Legolas and Arwen.
Merry would not have kissed Solaris' hand in greeting. He's a Hobbit, and he hasn't been brought up to act like that. That sort of chivalrous behaviour wasn't a part of their culture.
That last little bit didn't make much sense either. Still, maybe you are going to explain it in future chapters. It just makes no sense at the moment.
I cannot think for the life of my why anybody would want Solaris to sing at the council. They've got much more important things to be discussing. I'm afraid the whole singing thing is typical Mary-Sue behaviour.
Again, sorry if this review sounds rude. I'm really only trying to be helpful. For what it's worth you do seem to have quite a nice writing style, so your work could turn out quite good. If I thought this story was hopeless I wouldn't be spending my time writing concrit for it, so if anything take it as a compliment ;)
Ok, this isn't a flame. It's just constructive criticism, so please don't take offense.
Firstly, while your spelling seems to be mostly ok, there are a number of sentences that don't make clear sense. Your grammar could use some help to. I recommend that you get a beta reader who could help you sort out those problems.
Secondly, Elves do not have red hair. There's simply no way around it. They can have dark, blonde or even silver hair, but never red.
Solaris is simply not an appropriate name for an elleth. It means nothing in Elvish.
The whole branding thing is completely un-Elven. The Elves would never do that, even if they were some underground group like your assassins. It really isn't plausible. Oh, and the rangers were the remnants of the Dunedain, not some group that any person of any race can join. An Elf can't belong to the rangers, though some (like the sons of Elrond) may aid them in their missions.
So far, Solaris is a complete Mary-Sue. She's very unusual-looking (see my previous comment about red hair) and extremely powerful. She stands out from her race in that she's been permitted to join a group that only accepts males. Anyway, if it had been such a controversial issue to let a woman join their group, it would have taken a lot longer for them to decide. She wouldn't simply be given the brand just like that.
By the way, the notion of a group of assassins in Middle-Earth seems a little absurd. I don't think Tolkien ever mentioned anything about some elite group that were somehow better than all the powerful warriors and Elf-lords he created. Basically what it is doing is giving this girl something over all the Fellowship. Never mind that they (excluding the hobbits) are all fearsome warriors, Solaris is an assassin! It really doesn't work for me.
The Nazgul were sent out from Mordor to hunt down the ring. They are extremely unlikely to be gallivanting off around the country chasing assassins. And even if they did, the results of their attack would be fatal. They wouldn't just leave Solaris alive.
Legolas sounded like a little kid off for his first day at school, in the parting scene. And what's all that about Arwen loving him? Um, Arwen is in love with Aragorn.
I don't know much Elvish either, but your stuff doesn't sound at all like what I know of Elvish. I'm not really in a position to say, but it sounds like the translator you're using may be false. I could be wrong there, though.
Again, please don't take this as a flame. It isn't intended to be rude or cruel, I'm only trying to point out what I perceive to be errors in the story.
One final thing; you shouldn't post an entire story all at once, as far less people are likely to take the time to read it. Much better to submit it one chapter at a time, even if you've got it all written. And your summary isn't particularly eye-catching at this stage. I'd recommend changing it a little to make it sound more interesting.