"freie Medien" et al are idiomatic. "frei" still subsumes "kostenlos" in the general case (e.g. free entry). English has "gratis" or "free of charge", too.
Wait is "gratis" an actual, common English word? As a Spaniard I thought it was a joke kind of thing or used in extreme cases to differentiate, but that it was not really used in English (it is a common word in Spanish).
Its not uncommon in my experience as a native speaker. I feel like the context of gratis is more transactional than the context of free; eg. "Its a free country" makes more sense than "Its a gratis country".
Because that's not how gratis is used. In analogy to "persona non grata", that would be "America is an acceptable country". It may be gratuitous or gracious, however.
Similar to "libre".