Sorry to make you manually type all that information - I thought you'd be able to just cut and paste.
Anyway, the information was important - thank you.
This is the problem:
'/user/DATA/mysql/mysql': No such file or directory
It needs a directory "/user/DATA/mysql", and it's missing, or cannot be written to.
You will need to be "root" in order to start and stop mysql. And you will probably need to be "root" fix the "/user/DATA/mysql" problem, too.