Terminal input wrong behaviour

Basically, I have a very strange problem - when I ssh into the machine running CentOS and I open some file in nano to edit it my terminal behaves like crazy.

When I delete something it can put either a simicolon or a closing parathesis or actually delete the thing I want.

Also, the cursor can jump from one place to the other when pressing left/right key. This jumping is only along the line.

Finally, when I press left/right some characters may be overwritten by the characters from the other parts on that line where the cursor happened to be.

It almost seems like the wrong commands are being sent.

Last thing – which is not related to the terminal – if I put mission control to be triggered by Ctrl+Right I can trigger it ALSO by pressing FN. It seems to me that something is very wrong with how character input is being interpreted... Although I do not have ANY problems when typing in other apps.