Fast-setting repair glues list drying times of about 10–45 seconds. School and craft glues are noted to dry clear but typically don’t specify such short, seconds-range drying times.
Some repair adhesives are labeled water-resistant or waterproof; one product specifically notes the bond remains secure even when exposed to water.
Listings cite adhesion to paper and paperboard (cardboard, foam board), wood, fabric, ceramics, plastics, metal, rubber, leather, and craft materials such as foam sheets and craft sticks.
Yes. Some school glue sticks and kid-focused glue tubes go on purple so you can see application and then dry clear.