Tengo miedo is literally translated as I have fear. That is grammatical, but weird, English. Duolingo, rightfully, translates it to the normal English sentence, I am afraid. I am not worried would be No estoy preocupada (or preocupado). The basic meaning of Tener is to have.
I suppose it is possible to regard translation as a two-part exercise: word-substitution, followed by the addition or omission of words 'to make it sound better.' But in pursuit of fluency it is surely more efficient and less frustrating to consider the meaning of the sentence in the source language, and then express the same meaning (as nearly as possible) in the target language. In English, in a negative construction, we normally use 'any' to express a lack of something (sisters, money, worries, etc) -- and 'some' in the affirmative. To be sure, you can sometimes get away with omitting 'any', but its inclusion is usually more natural.
Similarly, the sentence "I am afraid" is normally expressed in Spanish as "Tengo miedo." It's not that "tengo" means "I am" in this case, and "miedo" means "afraid." "Miedo" is still a noun. The two languages simply have two different, but equally logical, ways of expressing the same idea.
Correct me if i'm wrong - but expressions like "Tengo frio, Tengo hambre" etc all translate to "I am cold, I am hungry" which in English is more correct than, "I have cold" which is rarely ever said. Is this exactly the same expression - No tengo preocupaciones = I am not worried? Which Duo marked as incorrect. Thoughts?
It sure sounded like the speaker said "precopaciones" even though I knew it was supposed to be "preocupaciones", which is what I wrote before I listened to it a third time! Does anyone else have trouble occasionally with the computer lady's pronunciation or is it just my problem?
spanishdict's page for "any", http://www.spanishdict.com/translate/any, has this usage note: 'When "any" modifies an uncountable noun or a plural noun, it is often not translated into Spanish.'
So when translating from Spanish into English, we can add the "any". To me, it feels more normal to add the "any".
I think reservations would be a good colloquial translation. If you were translating meaning that would certainly work, but as for a literal translation, no, I don't think reservations would be a good one. I'm sure there's a word in Spanish for reservations, I don't know what it is, but I'm sure it exists. Probably 'no tengo ninguna reservaciones'