You don't take mana burn if you tap out at the beginning of your upkeep and do nothing until your discard phase, where you spend it all on an instant.
I'm pretty sure that's not right. I know it's phase oriented. In fact, you cannot float mana to your draw in 4th ed. because draw was a phase back then, and you could respond to the actual drawing a card (this was when you used VT and such to make sure a shuffle effect couldn't fuck you over). I seem to remember taking mana burn in Shandlar at the end of my first main phase when I declared attackers.
You're incorrect on the Lightning Bolt. You die at the end of the upkeep phase. It was a great trick back then to cast Psionic Blast targeting yourself, activate Mirror Universe, and then your opponent would lose at the end of the upkeep phase. There was certainly no rule that said "you can't lose during the upkeep." I know for a fact that numerous games were ended with Mirror Universe at the end of upkeeps.
You couldn't play spells during untap. You could tap mana and burn during that phase (Mirror Universe tricks once again), but that was it. If damage was done, you could play damage prevention spells, but that was about it.
I think I still have an old rule book lying around somewheres.