Are dikaryotic fungi always heterokaryotic? ... ?

Dikaryotic does - by definition - mean that there are exactly two nuclei in the cells, it does not say that the two nuclei are genetically distinct! heterokaryotic does also mean only one thing: the nuclei (the number is not important) are genetically distinct.

that's the reason why, for example webster, writes "heterokaryotic dikaryon".

in fact the nuclei are distinct in almost all cases, that's why some only write "dikaryon"

Yes I think so. For being dikaryotic, the nucleus has to be compatibile (and the factor is usually associated with a single locus and hence they are usually describes as + or - ) with each other. And the compatibility factor present in the locus seems to dictate whether the hyphae will come together and the walls will dissolve. So if its dikaryotic its nuceli has to be heterokaryotic (i. e the nuclei are different from each other). The compatibility factors seem to dictate whether the fungi can mate. seems to be like a fail safe tojsut prevent hyphae with the same genetic makeup form mating with each other.