If it is adjustable from a depth of 12 inches to 18 inches, then is it still 8U at both depth measurements??

Yes that is correct The entire rack mounts on both sides slid out to change the required depth.

Can the built-in shelf of this server rack be adjusted, and if so, where can it be positioned?

Yes, the built-in shelf can be positioned at either the top or the bottom of the rack.

The maximum weight capacity of the StarTech.com 8U Wall-Mount Server Rack is 75.20 lbs.

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StarTech.com 8U Wall-Mount Server Rack with Built-in Shelf - Solid Steel - Adjustable Depth 12in to 18in

Mount your server network and telecom devices to the wall while storing your non-rackmountable equipment on the built-in shelf
Works with rack mount devices such as servers network & telecom equipment
Wall mount rack / Wall rack / Server Rack with wall mount shelf / Network rack / Wall-mount rack / Server rack shelf
Built-in shelf can be positioned at either the top or the bottom of the rack
Save space in your office or server room by mounting equipment to a wall
8U wall-mount design