I have backup storage on FTP server. I want to mount FTP server (may be with a help of curlftpfs) ands not only read/write, but also execute shell commands there, too. Is it possible?
There's nothing that will mount and let you execute remote shell commands.
But the mounting it simple enough:
sudo apt-get install curlftpfs curlftpfs ftp://username:password@server /target/
You can then run local shell commands by
/target/ (obviously change that in both cases to somewhere you'd actually like to mount it) and then run whatever you want.
If you need to run remote FTP commands, you're best off with a proper FTP client like Filezilla.