How to read STM32F407xx Microcontroller Power Schematic?
To answer just your specific questions:


  What does 15 X 100nF actually mean? Why do I need FIFTEEN capacitors .. what does the notation 15 X 100nF + 1 X 4.7uF mean?


They want you to have one 4.7 uF capacitor (aka "bulk capacitance", like a beefy storage tank) to main VDD rail, and then for each VDD pin they want you to put one 0.1 uF cap to GND near that IC pin. From the diagram, it seems like if you pick the package with the highest pin count (176 pins) it will have 15 VDD lines. The smaller packages would not have as many VDD pins so you can use less than 15 0.1 uF capacitors.


  what do the dashed lines to the left of the ADC right by VREF+ and VREF- mean? 


It means you can use either the VDD rail or an external VREF+ voltage as your ADC reference. If you use an external voltage reference, you should add a 0.1 uF cap in parallel with a 1 uF cap to filter it.

They put dashed lines to mean that you cannot obviously connect it to both at the same time. Pick one.

External VREF+ can be very helpful because VDD can bounce around and have noise which makes your ADC readings noisy. By using an external voltage reference IC, you can get a very accurate voltage and low noise because no other circuit loads it down. Also, these references are available in handy binary related numbers like 1.024 Volts, 2.048 Volts, 4.096 Volts, etc.