Venting a double kitchen sink (converting from an S trap to a P trap with AAV in a tight space)
In your 4th photo you have the sanitary tee oriented improperly ( horizontally instead of vertically ) but in your 6th photo you have it correct ( but you have an incorrect fitting on the top ). 

The sanitary tee will sit on the straight drain pipe going down through the bottom of the cabinet, it will accept the pipe coming from the trap. Depending on space you may not need to take such a circuitous route to get the trap outlet into the san tee. ( Meaning you may not need the 90 elbow going into the san tee, the trap swivels and you can cut the pipes to try and make a straight run to the san tee ) 

For the AAV you can come off the top of the san tee and then 90 over to the side of the cabinet and then 90 up so the AAV can go up between the side or back of the bowl and the cabinet ( anywhere there is room for it. ) 

It needs to be a high as possible. Put a threaded connection just after the 90 that turns up so you can pull it out if you need to change or service the AAV in the future.