Is the structure of the protein that makes other proteins (rna->proetien) known?
Yes, the amino acid sequence of a protein is usually the first piece of structural information obtained. It often comes from sequence the gene (in DNA) that encodes the protein.
If so, couldn't you accurately predict what would happen as each amino acid gets added?
This might work if proteins formed some sort of linear structure, like maybe a string with an occasional small knot. Proteins aren't like that; they form one giant, intricate knot. Removing/Adding/Mutating even a single amino acid can prevent the protein from folding. The interaction between amino acid 14 and 352 is often far more important than the one between 14 and 15. It's kind of like a puzzle that you can't even start to make until you have all the pieces.
Create a model containing the protein maker, water, and add the aminos into the "input" part of the protein maker and keep track of the forces. Wouldn't this be better than just rolling out thousands of somewhat random shapes and testing them?
Yes, it would be better. By modelling the protein and solvent, you will be able to observe the complete folding pathway for the protein as it goes form an unfolded- to folded-state. You'll get the whole play-by-play. Watching the process would provide fabulous new insights into which part of a protein folds first, what the key interactions are, and could very well suggest what modifications could be made to make the protein more--- whatever you want it to be: stable, flexible, faster-folding. Unfortunately, computers aren't fast enough and our molecular models aren't sufficiently well-developed to allow this. The models we have for molecular interaction on this level are primarily empirical (this ain't quantum physics) and are therefore limited to our ability to measure nature. Nature doesn't particularly like being approximated (how precise is the 7-day weather forecast -- how often is it right?).
Because modelling on this level is so difficult, we take shortcuts to find the final structure. Guessing at structures and then checking them for stabilizing interactions is one method that is being tested.
On a tangent, one of the biggest problems in protein folding is modelling the way in which a protein interacts with water. Water is (for a liquid) very structured and its desire to structure is one of the primary driving forces for protein folding.