Nice ...
I have copied it for future use... 
Tom... 
Can the Vin pin be used, yes, it depends.
Using the Vin is quite acceptable if you are only powering the circuitry on the Arduino PCB, and maybe a light peripheral load. The Vin pin should be powered by 7 to 9v to keep regulator heat to minimum.
In the below example the servos are being powered by 4 AA batteries (6v). These servos will work down to 4 to 4.5v.
The Pro Mini gets its power from a Boost Converter powered by these same batteries.
If a Buck Converter was used and set to output 5v and this was sent to the Pro Mini 5v pin, we start to starve the Arduino when the batteries get below 5.2v
Instead the onboard Boost Converter is set to 7-9v (8v in this case) and the Pro Mini is powered from the Vin pin.
Could we use a Boost/Buck converter, yes; these, however, are very large and over kill as the Arduino can be powered by the Vin.
And yes, modern day Boost and Buck converters are almost always the answer to powering projects today as their efficiency is so good and in this case only cost $0.50 each.
I saw your first schematic and i thought hmmm. I would just do it like this : 
And then during the editing i noticed ... the 7808 has both sides connected to GND and none to 12v+
If you put a capacitor before the 7805, you want to make sure that the PUMP doesn't draw from it. The 7805 can provide up to 1A (or is it 1.5A ?) and all it really takes is a sufficient heatsink if it gets to hot for what you are doing, But a TO-220 package probably doesn't even need one.
Thanks to all!
@Deva_Rishi : yes,I noticed my fault with 7808, signaled by @runaway_pancake in a previous post. Thank you!
Ciao.
Giuseppe
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