"What is your manager's name?"
Translation:Care este numele managerului vostru?
Why "care" and not "ce"? I keep asking this question to Romanians and everyone gives me another answer. None of them match this sentence expect for my manager's answer, who told me I should forget about a rule and just start talking... Not so sure that gonna work not living in Romania. Does anyone have a better idea?
Actually I think this was the very first explanation I ever heard on this topic and it would match this sentence here.
But I tried to apply that rule to other sentences and people told me I was wrong.
e.g. I tried "Care culoarea are cartea de dedesubt?" and my friend told me it had to be "Ce culoarea are cartea de dedesubt?" with the reason, that I didn't specifically mention the specific choices before, although I would have guessed it's clear that there are only four distinct colors in a deck of cards.
Another example what a collegue said to me: "Eu i l-am cerut Dorei care acum e in concediu." Here I would think, that it's neither a definition, nor a choice, it's just a description of Dora's current state. What I understand from what I was told when I asked about that is, this description usage of care and ce is maybe a thing of its own and means I have to use care for people (or personified animals or objects) and ce for anything not seen as a person. On the other hand: "Am modele vechi, care doar se deschid." would already disprove this idea...
Okay, the confusion arises from the fact that you are conflating every possible function of "care" with every possible function of "ce", and then trying to figure out when to use one over the other. You won't get anywhere with that approach.
The discussion for the current Duolingo sentence is about "care" vs "ce", but only in the context of questions like "Care este [...]?" vs "Ce este [...]?", the explanation being that the first one implies a choice and the second one implies a definition.
For other sentences, the rules will be different, because the purpose of "care" or "ce" in the sentences will be different, compared to what I described in the previous paragraph.
In your example with the playing cards, you can see that there is no "este" after any of the two words, so the sentence structure is a bit different, and the function of "ce" is different. The correct answer in that case is "Ce culoare are cartea de dedesubt?". If you really want to use "care", you have to rephrase it in order to use the form with "Care este [...]?", so you would get "Care este culoarea cărții de dedesubt?".
In your example with Dora, the word "care" translates to "who", and does not imply any choices, definitions, but specifies Dora's state. In this type of sentences, you can use "care" for everything (persons, animals, objects etc., regardless of whether they are personified or not), but you can/should use "ce" only for non-personified things.
I have no idea. There's a general shortage of good Romanian resources on the web. What you could do is look over the books listed in the "FREE Romanian Resources" sticky (2nd and 3rd bullets from the "Grammar" heading). You could read section 3.4.7 in the Cojocaru book, and the "Interrogative-Relative Pronouns" section (pages 20-22) in the FSI book.