How on earth should one distinguish tallerken and tallerkenen on this one - or generally?
You can distinguish between them by the missing indefinite article: "Han har tallerkenen" versus "Han har en tallerken". "Han har tallerken" is just wrong.
It is a bit difficult when spoken - most dialects, unless over enunciating, will 'eat' most of the '-en' ending. Listen out for the protracted nn-sound - that'll be it.
I am starting to get an ear for the subtle sound made by the definite-suffixes, but I don't understand why a lot of times consonants like "k" or "g" will be silent. I've found a couple good youtube videos that explain consonant sounds in detail, but generally they forego explaining when they're meant to be silent.