The insect species that lays its eggs in a straight line is the stick insect.
The insect that lays small, hard shelled white eggs is probably an ant that is black in color. This type of ant is commonly called a carpenter ant. Carpenter ants like to lay eggs away from the nest in warm, damp places.
giant water bugs
that would be termites
None do, what you heared or assumed is a myth.
An insect called Bed Bugs
Greenhouse Whiteflies are a pest that can occasionally be greenhouse pests. The greenhouse whirefly lays their eggs in a circular pattern.
No, its an insect - it has 6 legs and lays eggs.
The Cicada
The painted tiger moth is an insect lays bright blue eggs. Most of the time they lay their eggs in shrubs so their baby caterpillars can start to feed right away.
The insect that lays orange eggs on ferns is likely to be a type of ladybug known as the orange ladybird (Halyzia sedecimguttata). These ladybirds are commonly found on ferns and their eggs can be orange in color. The larvae of these ladybirds feed on aphids and other small insects found on ferns.
The female Lesser Water Bug fastens her eggs on the back of a male with glue. Other insects place eggs on plants or underneath the soil.