Accident causes physical damage to child: legal proceedings?

I would appreciate feedback from anyone with similar experience and/or expertise in the field of accidental damage (physical damage to the body).

The incident took place at a night market while buying foods from a vendor. A child got burnt with oil (1st and 2nd degree burns).

I would like to follow through with legal proceedings in order to get compensation for damages, have the sub-standard safety environment upgraded at the specific site and possibly have the vendor contribute to an association/funds that deals with victims who got burnt.

Please email me at zarbiz@lotushill.com.tw

Thank you for your attention.

J Reichert