Is there any shortcut for it?
If not is it possible to set a key for this operation?
I am using Ubuntu 14.04 LTS.
yes you can using Ctrl + D as you can see in this page under the Shortcut keys for editing files: Gedit shortcut keys
Yes. Position the cursor anywhere on the line you wish to delete and hit CTRL+D.
Apparently the shortcut is simply built-in into Gedit. I can't find an easy way to change it; apparently that's technically not possible [anymore], or at least not easily.
For anything related to text in general:
Use Home to put the cursor at the beginning of the line then Shift+End+backspace
Similarly you can set the cursor at the end using End then Shift+Home+backspace