Learn English – use “consistent with” in this way? If not, what can I use instead

lepidopteran

This is both an adjective and noun, and relates to Lepidoptera:

An order of insects that comprises the butterflies and moths. They have four large scale-covered wings that bear distinctive markings, and larvae that are caterpillars.

Butterflies flit (in an apparently unwitting way) from plant to plant to feed on nectar or deposit eggs, while moths typically are attracted to bright lights at night. Neither butterflies nor moths do any research.

A Google Books search reveals that the term lepidopteran has only ever been used in a scientific context. For example, page 134 of Insect Pest Management notes that:

There are no recorded examples of vertical resistance to Lepidopteran pests which have a strong flight capability...

The metaphoric use of the term to describe people who post very similar questions asking for the same words without doing any previous research has no precedent. It would be used in a sentence thus:

Oh no, here's another lepidopteran post.

With your first set of examples, either are correct. I believe It is quite reasonable construction. I think you're struggling in that the first part of the sentence sets up an indirect question:

One question you could research is whether female birds mature faster than their male counterparts.

As for the punctuation, this is a style issue. Either of your constructions would fit with The Chicago Manual of Style

In your bonus example, you are stating an indirect question so the punctuation is correct in the latter case.

One question you could research is what impact doing ten jumping jacks a day has on lifespan.

Still this is confused by using what because typically what is a direct question word. You're better off rewriting in this case:

One question you could research is the impact of doing ten jumping jacks a day on lifespan.