Are insects animals?
YES.
Insects are Arthropods which are invertebrate animals having an exoskeleton, a segmented body, and paired jointed appendages. They are classified under the Kingdom Animalia.
Arachnids (spiders, scorpions), myriapods (millipedes, centipedes), and crustaceans (lobster, crab, shrimp) are also Arthropods, and therefore also animals.