Re: Anna's game style ?
Chakvetadze has solid strokes off both wings, although her backhand is probably a little better. It's hard to tell since she's so consistent in all of her shots. Sometimes her serve can break down, or she'll go into error mode, but she's the most consistent top 20 player aside from arguably Jankovic and Henin, but I think Henin's in a class of her own, so for now I'll say just Jankovic.
For how she plays, she's a steady defensive baseliner with very good movement who will use the angles, hit behind her opponent, and go down the line repeatedly (I cannot stress that enough, the DTL BH/FH are her favorite shots it appears) to make them run and get her in a position to win the point fairly easily. By that nature, she doesn't really go for her shots as often as she should, but because she can stay in rallies for so long she can usually just wait until her opponent hits an error.
Her net game is okay. Give her a basic punch volley to hit and it'll usually be a winner. The angles are the only touch part of her game I consider good. Her drop shots, volleys and smashes are not particularly effective but they can get the job done.
I'm an extreme non-fan but I hope this was an objective analysis of her game with its perks and weaknesses both.