It was a while ago since I played CS1 and 2, but lets see if my memory still works.
>Does CS1 at least get better later(chapter 2)
A little bit, every chapter follows the same structure though. But at least it get more interesting as things go on, and the music for some parts in the later game is pretty good.
>CS get better after 1?
I think CS2 is much better than 1, because 1 introduced all the characters and locations, so it doesn't waste any time reintroducing you to it and it also (Act 2) stops being linear, so you can freely explore the eastern part of Erebonia at your leisure.
The music overall is also better than 1.
Similar to CS1 in its linearity and structure. I think the plot and setting is a bit more interesting than 1 though.
Haven't played it yet, but I assume it follows a similar structure as CS2.
Besides, I think you will have completed all the CS games by the time Kuro rolls around anyway.