I've noticed that the lag is especially bad in Gridania.
I've only gotten to play a little bit on two different days, but in my limited experience Gridania was awful one day and fine the next. Certain graphics-intensive areas dropped frames no matter what, but I think it can be a highly varied experience. There's all sorts of opportunities for lag in this game--the PS3's aging hardware for one, and servers for another. I was personally rather shocked to see just how much SE had to scale back the graphics to get things as smooth as they are on PS3.
I will most likely want to transfer my character and use her when I start playing the actual game. Unless that is not possible? I just wanna keep my same name, lol. I didn't level too much, so I wouldn't mind leveling over again.
Not only is it possible, it's simpler than transferring. Just log in with the same account and boom, your character will be right there!