The order of layer precedence on your display (i.e., which layer appears to be “on top” of other layers) has no relationship to how the board will be manufactured. There is a fundamental assumption that a substrate material (usually fiberglass) will be in the middle of the fabricated board. Copper will be placed on both top and bottom surfaces (for a “two-layer” board). The whole board - except for certain specific areas, such as pads where parts will be soldered in place - will be coated with “solder mask” (also called solder resist). Silk screen (also called “legend”) will be placed last. Finally, a high-speed router bit will follow the “Edge.Cut” line (also called “Outline”). The cut is almost always made to the center of the Edge.Cut contour, though a few fabricators may still route to either the inner, or outer, edge of the edge.cut line.
The Gerber file format intrinsically supports this fabrication process, since each Gerber file contains information for only one “layer” of the design. The Gerber file for, say, top silkscreen contains ALL of the information for the top silkscreen layer, and ONLY information for that layer - regardless of how the layers may be displayed in the program window. This fabrication process is a fundamental, underlying assumption between the designer and the board fabricator. Sort of like buying a tire - both you and the tire seller assume the tire will be basically round, without any corners on the tire.
The other layers, such as “Courtyard”, “ECO”. “Paste”, etc, are generally irrelevant to fabrication of the basic board. The “Paste” layers contain information for creating stencils used when depositing solder paste during reflow soldering of a populated PCB assembly. “Courtyard” is generally used to guide the board designer when placing components near to each other - the information on “Courtyard” depends on the exact process used to populate and solder the complete PCB assembly. There are other threads on this Forum where users discuss how they use the remaining layers (Dwgs, ECO, etc.).
Dale