Is this bag carry-on size?

At about 56 cm long it exceeds the typical 55 cm carry-on limit on many airlines, so check your carrier's rules. It is more likely to work as a checked or secondary bag.

Does it really fold flat?

Yes, the soft PU shell and lack of a rigid frame let it collapse for storage. Expect some creasing in the material after it has been packed tight.

How much can it hold?

The listed capacity is 36–55L, which covers a weekend of clothes or a large amount of shopping. The upper figure assumes you overstuff it, which stresses the seams.

No. PU leather resists light splashes but is not waterproof, and the seams are not sealed. Use a rain cover or dry bag in heavy weather.

Can it be carried on the shoulder?

It has carry handles, and the soft body can be slung over a shoulder, but there is no padded shoulder strap. Long carries get uncomfortable when full.