How would history be affected if Britain was never invaded by barbarians or Normans?
I don't know what do you mean with barbarians but if Normans don't invade England, leastly English is totally different as OTL. And it affect greatly for history of France and England. Some wars there might be but probably not 100-years war.
What do you think would happen if Toba erupted in 1815 AD?
If Toba eruption is delayed with multiple millenia, our world would be very unrecognised world. But if Toba would has erupted 200 years ago, we would still be recovering from that if human kind even would survive from that.
What would happen if it were the Eastern Roman Empire that fell into ruin, not the West?
Seems bit implausible if Eastern Rome would fall but Western not. Eastern Rome was quiet powerful but Western Rome very weak and its collapsing was probably just question of time.