I have often seen ”とても” translated as "very" in English. However, I also have seen direct translations (automatic translations, so I don't know if this still applies) where what is being translated, makes ”とても” seem more like an adverbial or adjectival modifier which could be directly translated as "very anxiety" (from とても不安) or other such like phrases. Was the previous example just a mess-up from the translating software, or is ”とても” more just a modifier for either adjectives or adverbs that denotes a more extreme version of the word it is modifying?
You are correct, in fact it can be used to signify "very" as well as describing something extreme, such as your example of とても不安. I tend to see とても used a lot in writing, whereas in speaking Japanese people will use すごくmore than とても. Using とても is correct, but I think it depends on the region of Japan as well because not all dialects will use it. I rarely heard とても while I was living in Osaka.