Does the down payment also reduce IOF, not just interest?
Yes. Credit IOF, under Decreto 6.306/2007, applies to the financed amount, not the vehicle price; in the R$ 80,000.00 example, IOF drops from R$ 1,351.08 to R$ 1,050.84 when the down payment rises from 10% to 30%.
Is it better to put more money down or stretch the term?
They are different effects: the down payment reduces the principal and, with it, IOF and total interest; a longer term on the same principal reduces the monthly installment, but tends to raise total interest paid, because the outstanding balance accrues interest for longer.
Why does the interest saving exceed the extra amount put down?
Because every real less in principal stops generating interest across all 48 installments of the contract, not just once; in the example, R$ 16,000.00 more in down payment avoids R$ 8,030.24 in interest accumulated over the 48 installments.