Yes, but perhaps not as fast as with the UV light. Sunlight does contain UV rays. The atmosphere blocks all but about 3% of the UV radiation emitted by the sun. Exposure to UV rays causes sun tans and helps the body to manufacture vitamin D; overexposure causes sunburn and can lead to increased risk of skin cancer.
Depends on the glue in question (diffrent glues span from "in seconds" to "maybe if you leave it out in the sun a really sunny day". Check with the manufacturer or spec sheet.