Identify current mode of a file
 

I need to ftp file called "big" to different server
How should I find out when the file is in writing mode or not

What do you mean? Check if the file is being transferred or check if it can be written (permissions on server)?
Check man ftp for possible commands.

Sorry, but get the feeling that this is some kind of homework.

You can be sure that the file is in writing mode or not, whatever "writing mode" is.