"Is there" versus "Are there"

Are there any questions I should be asking?
Is there any articles available on the subject?

My instinct is that in the two questions above, it should be 'are' as the subjects of the sentences (questions/articles) are plural.

However I also recall being told that the singular 'is' is valid here too, and of course see it very often in usage online, and this has left me a bit unsure.

Update: I have stumbled upon the reason for the confusion.

Is there any water?
Are there any questions?

The sentence structure is the same but of course water is not plural, although it is not singular either.

Solution 1:

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?

Solution 2:

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.