Who do you think the masked girl in the grand magic games is ???? any guesses ???

If by masked girl, you mean the hooded girl that Jellal is chasing after, then my guess is Lucy.

Also, in Chp. 300, the hooded girl struggled to write with her left hand probably meaning that the hand/arm with her guild mark was probably cut somehow?

I'm hoping for a new character. A lot of people think it is Lucy, but I just don't want to see time travel involved in all of this.
If not a new character then my response to her being Lucy, is why not Layla? Layla "died" on the same day that the dragons disappeared,and all signs point to them making a return, so why not her? We all suspect that Layla was somehow involved with the dragons, this could be a moment it gets proved.

most probarbly she's Lucy

Well...I really think it's someone from the future. My best guess is that it's Lucy. The girl apparently used her left hand to write in chapter 300, but she pulled the pen cap off with her mouth, her hand was shaking, and that guy said that she had messy handwriting. So I think that she lost her right arm or hand or something. If it really is Lucy from the future, maybe the enemy cut her arm/hand off because that's where her FT insignia is. If that happened to her...oh my god...

That hooded girl is possibly Lucy. Because:

-She cried when she saw Natsu from afar. That's make sense, because according to the spoiler for the upcoming chapters, before Lucy left with Zeref, she said, "A song to yearn. I will never meet NATSU again." I think she's happy because she can see Natsu again...even in the past time.

- She wrote with her left hand. Maybe she lost her right arm where she had her guild mark.

I think she's not Levy. because that girl doesn't have scar in her face. But, who knows? Maybe Mashima-sensei will troll us again :p

IT'S MILLIANNA!!!!

In my opinion I think it is someone form the future but not Lucy. I think it may be Levy form the future. Because Lucy isn't the sandle wearing type.