What is the overall end result of proteins and enzymes binding together?
At a high level, points 1 to 3 are reasonably correct, but 4 is only a special case.

Say we're at end of point 3. You get a protein. Some proteins are enzymes (the majority of enzymes are proteins), others are not. Example of proteins that are not enzymes would be, for example, hemoglobin, which is "just" a (very high-tech) carrier.

Now, each enzyme catalyzes (at a very high level) one reaction, which may or may not involve other proteins:


Reactions without protein other than the enzyme: for example, the cleavage of sucrose into glucose and galactose (two small sugars) performed by an enzyme called sucrase. Such reactions can assemble, cut and modify small molecules or large organic molecules that are not proteins (for example, starch, which is a large polymer of sugar, or even DNA itself)
Reactions mediated by enzymes, that act on non-enzyme proteins: for example, your digestive enzymes can cut proteins from food into building blocks (amino acids) that your body can use to build its own proteins. Similarly, some proteins can ligate proteins together, or add things on them (the proteins on the surface of cells are commonly modified with small sugar chains that control their activity).
Enzymes that catalyze reactions that involve other enzymes: since enzymes are proteins, they can be the target of other enzymes. A very well described example is the cascade of enzymes called kinases. When a cell is stimulated by a hormone, a kinase gets activated by addition of a small phosphate group. Once it is activated, the kinase phosphorylates (i.e. it adds a phosphate group on) another type of kinase, which phosphorylates yet another type of kinase etc; that's a way to amplify small signals.


So the overall result of an enzymatic reaction, regardless of whether it acts on other proteins or not, is usually either 


The conversion of a molecule into some other molecule (1 to 1)
The assembly of several molecules into a larger, new molecule (N to 1)
The separation of a large molecule into smaller fragments (1 to N)
The transfer of a fragment of molecule on another molecule (N to N)


Examples of these four types of processes when enzymes act on other proteins:


1 to 1: a "protein disulfide isomerase" can rearrange the topology of the so-called disulfide bridges, that connect cysteine amino acids together in the target protein. This allows a misfolded, non-functional protein to turn into a functional molecular machine.
2 to 1: a "ubiquitin ligase" can covalently attach small proteins (ubiquitin) to old, broken proteins and target them for recycling, thereby preventing the accumulation of dysfunctional proteins in the cell.
1 to 2: a "protease" can cut another protein into two smaller proteins
2 to 2: a "protein kinase" removes the phosphate from a small molecule called ATP, and sticks it on another protein