If I move a file on the same partition, while I am moving, should I update the reference count of the i-node to two (since I am first copying) and then decrement it to 1 again (when I delete the directory entry) ?
Or the reference count is untouched during moving?
No.
When a file is "moved", what's really happening is that the reference to the inode in the file naming layer is being changed, that's it. In fact, the file is not copied.
Realize that the file naming layer is purely for your convenience. The file system itself really only cares about the inodes. Even directories are, generally, a fiction of the file naming layer. (It is true that some file systems actually organize directories hierarchically at the file system layer, but this would not be true of ext2 and ext3, for instance).
While it is technically true that for an extremely brief period there are either no references or two references to the file in the naming layer, this is really an atomic transaction from the point of view of the system call into the kernel that is being made, so it effectively will not matter and will not be a race condition for you.