Currently I'm practising some pixelart drawing for games. But when I do anti-aliasing for lines, I don't know whether I should draw them by hand or just tick anti-aliasing box in photoshop. Could you please help me pointing out the differences between those two and advantages for drawing by hand?
Do you mean "by hand" as in go in and do each pixel of the anti-alias manually? If that's what you are referring to than yes that is exactly what you should do. For most things though in pixel art you leave that off entirely.
Say you have a gray cinder block you drew by pixel. The cinderblock is on grass. You wouldn't draw a lighter gray edge on the cinder block you would go straight from gray to green. If you do anything else you can outline in say a black or you can of course shade with different tones of gray but you shouldn't be going around the edge with a lighter gray to create an anti-alias - that is the exact opposite of what the "pixel art" style is.
Here is a nice tutorial on dithering that also illustrates the edge: http://kitted.deviantart.com/art/DITHERING-TUTORIAL-Basics-69747353