LED burning out due to high current?
I have a feeling that you've connected your LEDs directly between the Arduino's output pin and ground. You're not supposed to do that - most microcontroller's output pins aren't designed to drive the current required to light a LED. You might end up burning your microcontroller too. You might have been lucky to have a microcontroller that somewhat limits the output current to a level that was safe for the white LED, but not for the yellow one.

Regarding your second question, your white LED is as close to your yellow LED as as a Chevy is to a Ford. They're just built differently, and will behave differently. That's why each electronic component has a datasheet - and why each car has a manual.

Regarding your first question, exactly what's burning depend on each manufacturer's process. In case of doubt, assume it's toxic. But you're alive, so it wasn't probably that bad :-)