There are 20 kinds of amino acids commonly used in life forms (some exceptional cases use modified ones, but basically, there are only 20 ever used). I’d name them, but that’s boring to do.
All nitrogen found in amino acids comes from the reduction of N2 to NH3 by nitrogen-fixing organisms. When in water, the NH4+ made can then be incorporated into amino acids.
Of the 20 amino acids, 11 are synthesized from the intermediates in the citric acid cycle, a major energy-producing cycle present in all cells. The pathways for these are actually quite simple. The missing 9 (in humans) are called essential amino acids, since they cannot be synthesized in human cells, They must be obtained through diet. Eating pretty much anything with protein (plants or animals) yields enough of the necessary amino acids in the form of proteins, which are broken up back into amino acids and reused in the body.
Bacteria, such as E. Coli, can synthesize all the necessary 20 amino acids. Some of the amino acids we use are made in our gut by our very own slave population of E. Coli.
When we say an amino assid is essential, its sort of a situational thing. FOr example the urea cycle might produce enough arginine for an adult, but not for a growing child (which needs more).
As for the breakdown ofherbivores, carnivores and omnivores, I think what is essential and what isnt is somewhat species dependedent. I would venture a somewhat educated guess that ALL multicellular organisms must depend somewhat on diet or symbiotic relationships (such as gut bacteria) to provide some of the necessary amino acids. Bateria, as stated before, can make all of them, as long as they can consume a carbon source (glucose, for example), and plants (IIRC) can make them all from the CO2 that they respire. I imagine the bug-eating plants evolved from some sort of amino acid deficiency, but then I’m really getting into a WAG.
Now, as for whether we synthesise proteins: of course. We only eat protein in order to get the building blocks of protein -the amino acids. We break down every bit of protein we eat into its components, then carry those back to our cells and use them again to make the proteins WE need, according to OUR DNA templates. While we have pretty much every protein in common with other mammals, our own DNA will code for a better-suited one for us, and so thats what we use. Besides, we label our proteins in such a way that foreign ones get destroyed, assuming they are able to enter the cell in the first place (which doesnt happen).
The proteins we make are used for a bunch of things, I’ll leave it to you to read a biochem textbook if you want details. Basically, though, our cells can only function with proteins, since they do everything from copy DNA to make more, or to make RNA, to breaking down glucose for energy, to giving your skin that lovely colour.
Sorry if thats a bit random, I was skipping through a Biochem textbook (Stryer, 1998) and trying to get relevent info.