Dizerner, as I was answering your questions it looks like your post got deleted somehow. Haha, now I look like I'm talking to myself. Luckily I pulled quotes from you before your post was taken down:
Have more experiments been done like this and why not?
As mentioned in the animation, many experiments have since been done and new ones are still being done. In the 50s and 60s, lots of amino acid producing experiments were played with. Scientists were testing different atmospheres and environments to make sure all bases were covered. If you look in the notes under our video you'll find links to papers describing a few of those experiments. The photos of scientists at the end are photos of a few of the actual scientists doing work today. They are no longer testing amino acid formation, that puzzle is long solved. they are now looking at higher level questions as I'll explain below.
Do they understand the exact chemical processes that lead to the formations?
Yes! We now know the exact play-by-play reactions that produce bio-molecules! The reaction shown in my animation (inside the Miller-Urey brown water) is called the Strecker Synthesis. The animation actually shows it work the way it does in real life. It was a lot of work to make sure we got it right but we were working with a NASA chemist so we figured we'd go all out for unnecessary realism
Research has shown that strecker synthesis is responsible for amino acid formation in lightning simulations as well as in asteroid simulations.
What role would amino acids even play in a continued evolution?
Amino acids are the building-blocks of life.
NASA chemists refer to questions about biological building-block formation/sorting as "Type 1 questions".
There are a few groups of biological building-block molecules that make up living cells: amino acids, lipids, sugars, and nucleotides. These building-blocks alone are extremely complex and specific, therefore, their natural origin was a great mystery until Stanley Miller showed us how to start answering these questions through simulation experiments.
All classes of building blocks have now been shown, through thousands of experiments, to form readily in a wide variety of probable, young-Earth environments. Nucleotides are the trickiest. Last I checked we had only found one solution for their production so far and it's not very probable. Too many things have to be perfect for it to work.
Besides building-block formation, type 1 questions also deal with how these molecules, once produced, are sorted and concentrated in one area. This is important to know because before these building-blocks can even begin to do anything life-like, they need to exist in high, relatively pure concentrations.
Type 1 questions are almost all solved. Most scientists have moved on to Type 2 questions: How do we get these building blocks to form larger structures that are at least superficially similar to proteins and genes? In cells, building-blocks have the ability to combine and form larger structures. We want to see this outside of cells. Watch our animation on DNA to see how nucleotides make up DNA chains and how amino acids make up proteins:
https://www.youtube.com/watch?v=zwibgNGe4aY
Many Type 2 questions have been solved, but many are style a mystery. For example, the average protein chain in life is around 360 amino acids long. So far, In prebiotic simulations, we have only seen them grow to about 30 amino acids long.
Type 3 questions are about function, things like: How does useful genetic information develop from random chains of RNA?
Surprisingly, some of these questions are already being answered too:
http://www.ncbi.nlm.nih.gov/pubmed/24157838