Sorry, you are right, I am always dyslexic when it comes to population stars, I get them face about every time.
But you are wrong about the pop III stars, the supernovae laten about 10 million years. The stars themselves, several hundred million years. Otherwise, I'd pretty much agree that Iron was abundant enough 10 billion years ago to consider life beginning to take form. However, you mention evolution, how long do you think it took for life itself to evolve? How long do you think proto life might have needed to evolve into microorganisms, and then onto more complex creatures?
My opinion. (Concise version)
Considering the harsh conditions in the early universe, I suspect proto life might start forming into life maybe as soon as 4-6 billion years after the big bang? Then maybe another 2-4 billion years to look somewhat like life as we know it, then maybe another 2-4 billion years to attain what we would call intelligence? So my guess would be the first intelligence may have arisen as long as 5 billion years ago?
In my opinion, I also would favour the blinking on all over the place idea. Stars spread the blocks far and wide, there wold be species we never possibly could see out there no matter how fast you go. Building blocks for life are found throughout space.
I would find it odd if other life didn't exist in the universe because the universe is so HUGE. Now if life did advance to the level of space travel you also have to take into account how long would it take them to get to a planet like ours. Are they so advanced that they can travel at the speed of light ( which I doubt ) or did they figure out a way to get around the universe ignoring light speed travel altogether. Then again maybe there not traveling any real distance at all but are just jumping dimensions. Opinions?