Well-educated Indians use the words dear and dearest exactly in the same way as people in the UK or the USA do.
However, it is not uncommon to see some Indians prefix the word dear to an instruction or a piece of advice. Also, some Indians say 'Hello dear', when they could easily say just hello or hello xyz.
As far as I know, unlike some other common Indianisms, this does not appear to have an equivalent in Hindi, or in Bengali, which I speak. I cannot vouch for other languages. It is definitely not common to hear something like "Priya, is kaam ko karna hai" in Hindi.
As an Indian, I find the usage quite patronizing, (though it may not have been intended as such), and either ignore it, or tell the person so, based the situation, or my relationship with them.
It is, however, more common for Indians use the word sir or madam, instead of dear, in the situations described by OP, for example, "Sir, you need to do xyz", or "Hello, sir!", or while being defensive. I cannot make out whether we Indians are polite or apologetic.