Learn English – Does the word “coaxable” exist

Poaching is always illegal, so the adjective "illegal" is redundant. There is a (rare) word to describe this kind of redundancy: "Pleonastic". It means using more words than needed.

Many style guides recommend reducing redundancy in your writing: You should say "tuna" not "tuna fish". You should not say "the two twins" (since twins implies two) you do not need to say "new innovations" (since innovations are always new).

But pleonastic expressions are not ungrammatical, and some are very common and natural, especially in speech or less formal writing. Sometimes a writer will use a redundant word to emphasise a point.

There are three types of hunting: Legal trophy hunting, illegal poaching and subsistence hunting for food.

The author wants to emphasise and contrast trophy hunting, which is legal, with poaching, which is illegal.

As pointed out in comments, there may be situations in which there is a legal defence to poaching, such as "necessity". And there are extended or metaphorical uses of "poaching" which do not refer to illegal acts. However in the context of hunting, "poaching" would imply that the act was illegal and so in most contexts saying "illegal poaching" is redundant, but serves the purpose of emphasising a point.

It seems as if there really should be some common adjective to describe engineering things -- but, unlike so many other disciplines, there isn't. "Engineerical" is not a word, or at least not one you would use seriously.

There are several solutions to this deficit:

1. (As per Lambie's suggestion) rewrite the sentence using nouns:

   The questions on the exam can be about physics, math, history, or engineering

2. Use a semantically correct but stylistically awkward compound:

   The questions on the test can be physical, mathematical, historical, or engineering-related

3. Use an awkward repeating term that nevertheless preserves parallelism:

   The questions on the test can be physics-related, math-related, history-related, or engineering-related

Note that the use of "physical" to mean "physics-related" may be confusing, as the more common uses are:

physical (adj):
1 Relating to the body as opposed to the mind.
    1.1 Involving bodily contact or activity.
2 Relating to things perceived through the senses as opposed to the mind; tangible or concrete.