Q: Are these spider mites? Or baby assassin bugs? Or baby cave crickets? There appears to be at least two different kinds of critters here. I spray my citrus trees with insecticidal soap every other week.
A: The white things are shed skins of the live yellow-green aphids nearby. Aphids and spider mites are well-known pests of indoor citrus trees.
Insecticidal soap used every two weeks is too seldom but spraying more often risks burning the leaves.
Instead, try neem oil (click for sources).