This is just weird, I've never heard this saying being used in Dutch (as a native)
"Van tijd tot tijd", I've never heard that in Dutch, I think a better alternative would be "wel eens", as that's actually used.
- "Vandaag is het bewolkt en er valt in de ochtend van tijd tot tijd regen." (http://www.volkskrant.nl/media/uw-nieuwsgids-voor-woensdag-16-december~a4208720/) 16-12-2015
- "De ergste nood trouwens probeert de regering van tijd tot tijd te bezweren,..." (http://www.rtlnieuws.nl/nieuws/buitenland/venezuela-wc-papier-als-metafoor-voor-falend-regeringsbeleid) 07-12-2015
- "Dat laat onverlet dat je van tijd tot tijd punten moet aanscherpen of aanvullen als gevolg van de wijzigende omstandigheden." (http://nos.nl/nieuwsuur/artikel/2064108-reactie-ministerie-infrastructuur-en-milieu.html) 20-10-2015
Are all three of those expression interchangeable, or do they carry some subtle differences in meaning?
They are interchangeable, at least I'm not aware of any subtle difference. :)
I'm not sure gradually is the best translation for met de tijd. Correct me if I'm wrong, but I think over time is closer to met de tijd. To me met de tijd means that it will happen somewhere in the future and nothing is known about how often or to what degree it happens. Gradually (geleidelijk in Dutch) gives the idea that it either happens/increases continuously or continually (it happens multiple times in the future and that the amount of change and the intervals between changes are roughly the same every time it happens).
You are of course right. I wasn't trying to be precise at all but looking for a quick complementary explanation for the very fundamental distinction between over time and from time to time.
"Yes, it happens now and then" was wrong, according to Duolingo, but why?
It's not literally correct. I reported the same thing as something which should be accepted, it is the same meaning as 'from time to time' in English.