Spectracide Triazicide Insect Killer for Lawns is an insecticide and does not have any herbicides or fertilizers in it, so there should be no issues using this at the same time as or near the same time as a weed and feed product. Be sure to check the labels for any specific restrictions.
Yes per the product label for Spectracide Triazicide Insect Killer for Lawns you should water lawn lightly immediately after application for some insects and for others water grass thoroughly with ¼ to ½ inch of water immediately after application. Please refer to the product label for complete instructions based on your target pest. You can mow 24 hours after.