I have never had DL ping me for this before, and in fact I have grown used to this word order as DL so often offers it as a possible answer. "Have you ... ?" may be much more common than "You have ... ?" but I have no idea why DL has suddenly decided to mark the latter incorrect here. EDIT: An additional note: after redoing this lesson I have noticed in many other similar questions DL actually offers "You have ... ?" as the preferred answer, so I can only guess this anomaly is a glitch.
Generally yes, "Have you ever" would be as commonly used, if not more so, in the context you suggest. You could also add "before" to the end of the sentence to convey the same meaning. However, there are contexts regarding the near past where "ever" or "before" would not apply. Eg: a chef working in 2 restaurants on one night: "Have you cooked in that kitchen?" Far less likely, granted, yet plausible.
I can't speak for your region, but that has a different usage in regular English.
"Had you ..." is past perfect so it describes an action that occurred before something else in the past.
"Have you ..." is present perfect so it describes an action that occurred at some point before now (and could still be continuing).
The difference means that "Had you cooked in that kitchen?" requires some past reference point, either explicit or implicit. "Had you cooked in that kitchen [before it burnt down]?" while "Have you cooked in that kitchen?" does not.
It's easiest to explain it from scratch.
Demonstrative adjectives (this, that etc.) describe a noun and like other adjectives have to match gender with what they are describing. "Esa" describes feminine nouns - "Ese" masculine. So here it is "That kitchen" - "Esa cocina." As all Spanish nouns have gender there is no need for a neuter demonstrative adjective.
Demonstrative pronouns (this, that etc.) stand in for nouns and must match gender with the noun they are replacing. For example if we wanted to say "That oven is dirty" but we already knew we were discussing the oven we could say "Ese esta sucio" because the Spanish word for oven (horno) is masculine.
"Eso" is the neuter form of demonstrative pronoun. It is used if the gender of the noun is unknown or if it is standing in for an idea or concept. eg Eso es lo que yo pienso - That is what I think.