Alternative Power supply options

[DrYak]

The first thing I wonder Is whether it will charge with alternate power inputs,

It has an USB-C connector that can accept charging.
(It can also charge through the USB-C while turned off. I usually leave it turned off and plugged into my USB-C charger).

So in my experience...

such as USB power banks,

Yes, though it's better if the powerbank can supply 2.5A @5V.
Most USB-C can (usual go as high as 3A).
Some USB-A, like the one I'm using, can. Check the specs of the powerbanks. (Some only do 1A)

Otherwise, under load the Pinebook eats battery faster than the powerbank can charge it.
So you won't be able to actually charge the battery, only to slow down the discharge rate.

In that case, you'll need to leaved it idle or turned off for better charging performance.

a biolite stove, solar panels,

It depends on the rating of the attached/built-in powerbank. See above 1A vs 2.5A.
(I can't find any information about the biolite stove)

or a 12V car adapter

Buy an USB-C adapter that does 3A at 5V
or an USB-A adapter that does 2.5A at 5V ( <- mine works for me ).

( prefer not inverter ).

Keep in mind that, despite being laptop shaped, this thing has the internal of a tablet - it runs on ARM (from Rockchip) and sips power ~12W.
It only uses voltage at 5V (unlike big laptops which require 20V input and charge at 60W (3A) to 100W (4.5A) )
thus going through a power inverter is absolute overkill and inefficient.

Think more like charging a power hungry high end phone or a tablet.
Most portable situation you can dream of will definitely work for charging,
some (as long as the charger can provide the require 2.5 A) will even work for charging+using at the same time.