Arduino minimal power usage I know there is a lot on this subject on the net but i cant seem to be able to join the dots together. 
I am trying to make sensor system than can run for as long as possible if not indefinitely using an Arduino, and also to do so very cheaply. I have a £1 Arduino Nano clone that is running with sensor and alarm fine, but currently its runs off USB power from PC.

I have followed this guide to minimize power usage code side: https://www.openhomeautomation.net/arduino-battery/

And I have read that the Vin pin needs at least 7 volts to work properly, so 2 volts would be wasted in heat making a 5V level.

I have a 3.7V lithium cell 4300mAh so I thought I would need a step up boost module.

But it looks like the Nano can run using 3V. But the 3.3V rail is apparently made for external sensors, assuming I want a mixture of cheap/simple and high efficiency. Can i just hook a 3.7 lipo into the 5V rail of the Nano and a 5V solar panel (with diode) up to same point? Will this kill my Nano? 
If not, is it worth stepping the 3.7V down to the minimum the Nano can run with?

Underclocking is not an issue, it essentially wakes up every hour reads 5 sensors and if all is well (99% of the time) goes back to sleep for an hour.
Linear voltage regulators seem to burn the excess voltage as heat. And then what will happen when the battery dies off and is no longer 3.7 volts? And if my solar panel is around 5V in good light, if its partly shaded and only has 3.5 volts for example it would not charge my lipo to 100% capacity. Should I step up DC/DC boost the panel voltage to charge my cell. 

Guidance please.
Arduinos are for rapidly getting something going without having to know much about the underlying electronics and microcontroller.  As a result, some design tradeoffs were made for you, generally optimized for development simplicity.

You now have a different primary concern, which is low power consumption.  If that is truly important, then you have to design the system with that goal up front.  This means starting with the bare microcontroller, designing the electronics around it carefully to minimize power, and designing the firmware architecture to minimize high-power cycles and maximize sleep time.

You are asking where to strap the big engine on a Honda Civic to make a high performance racing car.  You can make a Civic higher performance, but to get really high performance you have to start with that goal from the beginning.