Hmm the truth is, they're used to saying "data is, media is" more often. Way more often. However, "data are" is preferred in formal and academic writing.

You can use either. Data can be singular or plural. Similarly: folk; family; types of fish

No worries - this is something that not every English speaker is sure of either. Though, formally you would use the word "datum" to refer to a singular noun, it is very uncommon for any English speaker to do so. Data is the proper plural form of the word, "datum," though in every day English most speakers don't use the word "datum" at all. We normally use the word "data" to refer to both the singular and the plural. For example: "Could you find me a piece of data?" Says the scientist to his colleague. Really, don't worry about having to use the word "datum" at all. We treat it as if it were singular itself. No one I know uses the word "datum" in every day language. No worries, however you try to use it you will be understood. I hope this has helped. Best of wishes for you!