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Always use the plural "are" with a plural subject (e.g. "question"), and the singular "is" with a singular subject (e.g. "article"), or with an uncountable subject (e.g. "water"). Hence:
Is there any question I should be asking?
Are there any articles available on the subject?
Is there any water left in the pond?
The following are never correct:
Is there any questions I should be asking?
Are there any article available on the subject?
Are there any water left in the pond?
You're talking essentially about a matter of formality. In everyday, informal (especially spoken) English, native speakers commonly use "there's" (and derived forms) to introduce either a singular or plural.
In more formal/careful usage, "there are" (and derived forms) generally appears to be preferred when the logical subject is plural.