Hinges

what kind hinge (name of the hinge) used in this product?

That looks like simple pin (perhaps steel) in a drilled hole and a couple of spacers (perhaps plastic). I don't know of a specific name for this simple arrangement. Nor for the compound hinge formed by the arrangement of three simple hinges to form a folding brace.

Addenda ...

In the Snap-Jack furniture

All the fittings, and hinges are stainless steel, and the magnets and keepers are nickel plated, the hinge spacers are plastic

So the hinges are basically exactly as I said above. The magnets are not part of the hinge itself.

Latches

I think [...] a rare earth magnet [...] was used as a hinge

In the Snap-Jack furniture, magnets are not part of the hinge - magnets are used to hold the furniture parts in the fully-closed and fully-open positions. Magnets are also used to help hold the chairs and tables into the wall-mount in the stored position.

Magnetic safety latches

These magnets are not part of the hinges.

Part names

All these parts are available separately from most hardware stores.

• steel rod
• steel or plastic washers (maybe spacers too)
• disk magnets (screw mounted or epoxy into recess)
• keepers (or use a steel washer and a short wood-screw)

I would use a drill-press with a table rotated 90° to drill the holes for the pins.