Oy vey. This just gets better and better.
Let's start with the height. 18" is fine for standard 6" depth drop in sinks. On some deep bowl undermount sinks, particularly with a garbage disposal, 18" high can be an issue.
Regarding the horizontal pipe out of the side of the tee, and the horizontal pipe poking out of the wall for the AAV. Florida Building Code, Plumbing, 2010 edition, 905.4 Vertical rise of vent Every dry vent shall rise vertically to a minimum of 6" above the flood level rim of the highest trap or trapped fixture being vented.
So, the flood level rim is the rim of the kitchen sink. And that horizontal pipe is not 6" above the rim of the sink.
Also, the kitchen sink will be what is known as "S trapped". As the kitchen sink drains, the water draining down the pipe will close off the path for air to return back to the trap, and the trap will self siphon. Same code, 906.2, paraphrased: ...total fall in a fixture drain....shall not exceed the diameter of the fixture drain, nor shall the vent connection to the fixture drain......be below the weir of the trap.
Chapter 2 of the same code has definitions. Do a search for Florida Building Code, one of the hits will be for a downloadable version of the code. You will probably have to download the individual chapters.