Qual è la differenza tra 1)It happened second time e 2)It happened a second time e 3)It happened the second time ?Sentiti libero di rispondere con un esempio.

1) Is not correct, you cannot say this.

2) & 3) are basically the same

"Yesterday, it happened a second time."
"When it happened a second time, I was very angry."
"On Friday, it happened the second time."
"When it happened the second time, I was very happy."

However, it is always "the first time" and "the last time" (not "a first" or "a last")
"That was the first time we met."
"2019 was the last time I saw him."

So, normally you use "the second, the third, etc." if you also know how many times it happened in total (when you know when "the first" and "the last" time was!