I have this PCB in development carrying a wemos d1 and a power shield, side by side. The last time I worked with it, was some time ago and I kinda forgot what my idea was.. now I am sure it was a wrong one
The shield has a terminal to connect the battery to. The shield does not have a switch.
If I want to switch off the power entirely. Must I physically interrupt the battery line with a switch, or is it also 'sufficient' to interrupt the 5V output from the shield and disconnect it from my board's 5V line?
I don't know if the shield itself will draw a significant amount of power if the 5V output is not connected. From what I could find on internet the used chip draws under 10uA if no current is drawn. So I suspect that disconnecting the 5v, suffices.
I do not know that much about batteries. With a 3.7V battery with 1000mAh capacity it would take roughly 1.000.000 uAh / 10uA = 100.000 hours or 11 years before the battery dies out by the idle current, correct??
Also, I want to use this PCB in a MESH network. Can there something be said over the power consumption in that mode? The leds won't draw more than 5mA at any time.
That depends on what you intended. If you want to eliminate any power consumption from the battery you must disconnect the battery from the rest of the circuit (which may be done by a switch).
If you just want to stop the program on the Wemos you can put the switch into that 5V connection. The step-up converter will still draw current from the battery but that may be acceptable to you.
No, the power is converted to 5V for the Wemos board and converted there to 3.3V again. The first step consumes about 30% of the hours (given it's a step-up DC/DC converter), the second step usually looses about 10% again (linear voltage regulator). That leaves about 7 years of operation if only running in deep sleep state (not realistic). In a realistic scenario you might get about 3-4 years if you wake up only for a few milliseconds once an hour.
Mesh networks aren't good candidates for battery operation. You cannot put the mesh nodes to sleep (they have to be always prepared to re-transmit messages), so the they will constantly consume several tens of mA, your battery will be depleted in less than a day.