"Where is the plate?"
In most inflected languages, the verb "to be" does not take the accusative because there is an implied equivalence between the subject and the object. In other words, because "Where is the plate?" is semantically equivalent to "The plate is where?", both subject and object are nominative. This is true also of adjectives, e.g., "The plate is blue." In most inflected languages, "blue" is nominative (the so-called predicate nominative). Of course, in actual usage this may not always hold--in English, we typically say "It's me" rather than "It is I," even though the latter is grammatically correct.
I'm not sure about this, but I believe it's Где тарелка(nominative) because there is no verb that acts on тарелка in this sentence.
From the notes of this lesson: Actually, whenever a verb, like "read", "cut" or "want" acts directly on some noun, the latter is a direct object. Such nouns take the Accusative case.
The nominative is used for the subject of a sentence, so there may be verbs. I think this will help you(some explanations and examples of the russian cases): http://www.study-languages-online.com/russian-cases.html
I hear "Ta-le-oka". I believe the issue is the way "R" is pronounced in russian. As children, when we can't say "R", it comes out mostly as a "w". From what i am told, with russian children it is more of an "L" sound. Trying to roll the "R" in тарелка is difficult and doesn't come out very easily (or eloquently). Hope this helps
I think with the context it's acceptable. But I guess that it's English courses here are kinda wrong, they are misleading. look here https://www.duolingo.com/comment/4571665 for me it sounds and looks silly when "the" is translated. I guess it's absolutely not necessary and even kinda weird.