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The electric strength between two parallel plates does not depend on its separating distance, and only depend on the number of charges the two plates carried. Therefore $\epsilon$ cannot be calculated by a random combination of $\Delta$V and r with this formula below:

$${\epsilon} =\frac{\Delta V}{r}$$

Therefore is it for a certain pair of electric plates with a fixed voltage difference, there's only one value of r matches the structure? If not, the formula above cannot be used to calculate E, since E does not change with its separating distance.

I have seen some electric plates questions that gives its $\Delta$V and r . Can we assume the $\Delta$V and r are matched, and CALCULATE the epsilon out of them?

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Yes you can calculate the electric field strength by $E = \frac{\Delta V}{d}$ with the $d$ the distance between the plates.

The charge stored on the plates is proportional to this same fraction if we would measure it so there is no inconsistency with your correct statement that the electric field strength depends on the charge only.

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