Is it possible to write to a file (on a disk) using JavaScript?

You can write cookies with Javascript, on newer browsers you also have an SQLite database to store client side data. You cannot store data in an arbitrary location on the disk though.

Yes, of course you can. It just depends on what API objects your javascript engine makes available to you.

However, odds are the javascript engine you're thinking about does not provide this capability. Definitely none of the major web browsers will allow it.