Hi - yes it is a nice representation of the layer stack however the only way of getting it into documentation is to use the copy button below it and then paste the image into a word document etc. Adding it to the design is not currently possible - I hope it will be in the future.
What you can do though is to make yourself a selection of documentation symbols that show your layer stack, perhaps with alternatives for different layer pairs etc.
Then you can add these to any documentation drawings.
Re the schematic symbol pins, the symbol itself has pin numbers I.E. 1,2,3,4,5 and in the part these pins can be mapped to the component pins so can show as 12,24,7,3,22 etc instead. Additionally in the part you can change the pin "number" to instead be an alphanumeric name I.E. A1, A2, B3 etc.