DC Power supply
Can the Prusa MINI+ be powered directly from a battery that delivers 22-29V depending on charge status?
What's the name of the connector they use?
Here are the image of the power supply marking and the connector: 
You will need to stabilise the voltage - there are converters available that will handle that for you at the expense of a few amps.
Cheerio,
RE: DC Power supply
What is the allowed voltage range?
Any idea for the connector name?
RE:
You might find more details at PSU datasheet https://deltapsu.com/en/products/adapter/ADT-150C24AC ( https://deltapsu.com/en/products/download/Datasheet/ADT-150C24AC)
The connector is a standard '4Pin Din'
and maybe something at https://github.com/prusa3d/Buddy-board-MINI-PCB
See my GitHub and printables.com for some 3d stuff that you may like.