In English these are all simply bugs. There is no cultural notion of good vs. bad, but there are a few expressions like snug as a bug that imply this.
I think bug is about as close as you can get, something like little bug works fine as a cute nickname. Otherwise there are only negative forms for insects, such as pests or vermin.
Instead of trying to fit one word for a class of "cute insects", you could choose a particular kind. This also makes it more personal and endearing. Consider:
- Ladybug (ladybird)
I can add that Czech also has the same idea of "cute bug" ("brouček") as a diminutive nickname, so I understand your question. There's no real equivalent in English.