Is it possible to create a file that will contain its own checksum (MD5, SHA1, whatever)? And to upset jokers I mean checksum in plain, not function calculating it.
Sure.
The simplest way would be to run the file through an MD5 algorithm and embed that data within the file. You can split up the check sum and place it at known points of the file (based on a portion size of the file e.g. 30%, 50%, 75%) if you wish to try and hide it.
Similarly you could encrypt the file, or encrypt a portion of the file (along with the MD5 checksum) and embed that in the file. Edit I forgot to say that you would need to remove the checksum data before using it.
Of course if your file needs to be readily readable by another program e.g. Word then things become a little more complicated as you don't want to "corrupt" the file so that it is no longer readable.