In reverse order . . .
4: Since you can't take up the offer of bringing your payment schedule back to where it was originally planned to be, there's not much point in concerning yourself over the missing letter ;
3. You can only make extra monthly payments, or extra at the end of the loan, if the lender agrees to it. Given that you weren't offered the chance to do so during your phone call, that would seem to be unlikely ;
2. Unless you can find the money to catch up with the original payments (perhaps by borrowing it from elsewhere) then, unless the lender suddenly decides to accept extra monthly payments, you can't avoid the default showing up on your credit record.
1. Your credit score only matters if you're actually planning on borrowing more money (e.g. through taking on a mortgage) or if, say, you're seeking a new contract for a mobile phone. Otherwise it doesn't matter at all.
A default would show on your credit record for 6 years. However you're entitled to add a brief explanatory note to any credit report:
http://www.creditcards.com/credit-card-news/help/add-written-statement-to-credit-report-6000.php