Well, you can give messages but can't chat like you can in a pc. Use the app 'facebook chat' (its free). It should do the work. 5130 is a s40 phone which means it's a java based phone. There would have little hope if it were a s60 symbian phone. I have that phone myself and use the app i mentioned.
No you can't. Only in ipads. and laptops..
yes you can.
To chat with your nokia 5130c download mozat it help to chat in multiple network.