Does your class need 1000 lines of code? If so then don't worry about the size of the file. Looking at the source directory where I'm currently working, there are 82 cpp files. 15 of them have more than 1000 lines. The largest is 9,742 lines. The class needs them all and there's no compelling reason to split up the file, so it stays as one file.
If you start to have over 9,000 lines in a file, chances are there might be something you could refactor into different logical parts, but sometimes it's just clearer to have a big file.
I will say though, if you are ever working with other people. it's sometimes harder to make changes to a file if it's a really popular file that everyone else is also making changes to. That's my (personal) #1 reason for splitting up files into finer logical parts.
If I add files to my class, for splitting member functions in shortest file, I receive error because class doesn't find implementation of methods that I bring to another file..
Are you including your class header file, and other required system headers, in each .cpp implementation file? From the errors it doesn't look like you are.
* The "undefined reference" is a linker error; no translation unit (given to linker) provides implementations for those members. You forgot to compile&link something.
* The "multiple definition" is also a linker error; multiple translation units provide implementation for same thing. ODR violation.