PCB stackup for an 8-layer PCB
To answer your questions:


Using thin prepregs is not uncommon, and in your case for example the standard 1080 prepreg is close to your 3mils thickness. ( a list of the most common thicknesses can be found here) 
The issue I see is that you are using a buildup construction, which non all manufacturers are comfortable with using. Another thing that is worth pointing out is that you have an asymmetric layer distribution, which means that you have the risk of having issues with the board flatness, after the assembly process. You might end up with a board that is shaped like a banana.


What I suggest is that you contact your manufacturer of choice, and get them to approve your stacking, making sure you specify what are the limitations that you require. 
That is the only way you will get the answer you need.