I do not particularly like this question because it is just hypothetical. The question could be asking for another random number and states no case scenario, but let's answer this so there is no misleading information.
What is the standard format to save very large images?
Very large images are not standard. They are experiments, they are technological challenges to prove a point, or to just explore some realm of technology or knowledge.
They are not one photo, they are composites.
JPEG's have a file size limit of 64k X 64k pixels
Let's explore the limit of 64,000 pixels.
You would need a 4096 Megapixel camera to take that photo. I only know cameras that can shot at 100-150 Megapixels, and those cameras are not cheap.
You need 33 FullHD monitors one next to the other to explore that image... to show only one row... You need 59 rows... or 1947 monitors (Yea, You could use 4K monitors but sounds less dramatic).
You would need a wall of 16m to paste an image of a good resolution of 100PPI... and you need 7 additional floors to paste the rest.
Modules. This is clear from the start of my image. You do a compositing later.
For an art exhibition, you print whatever the printer is capable of printing.
If the printer prints on a roll of paper of 90cm you use that, if it prints 1.5 m, you use that and composite later.
If you are displaying on a screen you use a zoom function.
If you are displaying again, in an international EXPO pavilion, you can split the signal, across different files and monitors.
What's the usual resolution or printing (pixels/inch) for such large images?
Again that is not usual, and again the image size does not matter. What matters is the viewing distance. The resolution is inverse to the viewing distances. For a distance of 60cm 150PPI, for 1.2 m away, 75PPI is good enough, regardless of the size of the photo.
The bigger the print, the further away you need to be to see it, so less resolution is needed...
A 24Mpx image can be viewed on your monitor close to your eyes, or a humongous billboard and still will look just fine.