With respect, I disagree with Todl here. This is not really a question of Tense.
Each of the original sentences contains two clauses. These are
CLAUSE 1 || CLAUSE 2
Did you know || (that) certain chemicals can cause cancer?
Did you know || (that) certain chemicals could cause cancer?
Do you know || (that) certain chemicals can cause cancer?
Do you know || (that) certain chemicals could cause cancer?
Firstly, let’s consider the variations on the first clause “did you know” vs “do you know”. Although we have do/did forms here, the fact is that English speakers often do not differentiate between the two in terms of meaning. They could both be considered to have the same meaning here, just as “I knew that” and “I know that” can be and are often are used interchangeably in English and can be used to mean the same thing in certain circumstances. We could only determine from the context if “did you know…?” meant “did you know at that time…?” , or meant much the same thing as “do you know…?”.
With respect to the second clauses, any and all of these could be interpreted as having meaning relating to the present. However, it is important to realise that these clauses are concerned also with Modality. That is:
..certain chemicals can (MODAL FINITE.: PRES. ABILITY) cause cancer
.. certain chemicals could (MODAL FINITE.: PRES. POSS.) cause cancer
(However there is one exception, and this is the second example. Context could determine that it is completely concerned with the Past. That is, “Did you know (AT THAT TIME) (that) certain chemicals could (MODAL: PAST ABILITY - NO RELATIONSHIP TO PRESENT) cause cancer?”. "Could" is a Modal Finite that can be used to express either Past Ability or Present Possibility. )
The only way you can come up with what one might describe as a purely “Present” sentence here is to eliminate the Modality and so come up with:
Did/Do you know certain chemicals cause (TENSE FINITE: PRES.) cancer?
