Did they give you any feedback on why you failed? If it's a personality thing then you may struggle, as this is difficult to change, and the philosophy of aviation these days is pushed so much to CRM and the right personality types, if there is a fundamental flaw you may never get on.
On the other hand, it may be a sort of go away for a year and get some more "life experience" and we'll look at you again when you have matured a bit or whatever.
The few hours you plan to fly probably wouldn't help you with any airline, other than to show that you are indeed interested in flying. It will probably be more use to you personally, as you have stated yourself, to be sure for yourself that you definitely want to be a pilot.
To answer your final question, yes you would need a working visa to instruct, so you should do the licence/instructor rating that is relevant to the country you wish to work in as a flying instructor.
Last edited by RTN11; 22nd July 2013 at 22:38.