I have got damage because of chmod values. I used to set directory chmod values to 775 in order to write/delete the files and folders. User was "me" and the group was "www-data". then I have been attacked and many files which try to send spam e-mail were written almost all directories.
Then I set Joomla's configuration to use FTP rather than HTTP for file transfers.

Everything works well. I can upload and delete any files using Joomla's Media Manager. But now K2 does not work. I try to add an attachment to a K2 item. It says "It is uploaded" but it does not in fact. I cannot see the file in the media/k2/attachmetnts directory. Besides, if I click on the attachment link at the bottom of the item, an error message shows up saying "K2 file does not exist".

If I set CHMOD values to 775 and set user to "me" and group to "www-data" it uploads and work well. But this comes with a huge security vulnerable.

My question

How can it be possible to say K2 to use FTP for file uploads?

This problem occurs for user image uploads too.

It adds a record to database but cannot write the file to corresponding directory.

You can use an extension like Admin Tools to correct your file/folder permissions.

The correct permission would be 755 for folders and 644 for files. If you are having issues with these permissions, then you need to address this issue to your hosting provider. This indicates an error in your setup.