Example 1
"I check "the" milk prices whenever I am in "a" supermarket."
What does the "the milk prices" refer to?
Does it refer to the milk prices in the "supermarket" in the whenever-clause?
Does that mean definite article can come first and indefinite article, the one being referred to, comes later like Example 1?
The choice of article has nothing to do with the order in which they appear in a sentence. Broadly speaking, we use the definite article for something specific or unique and the indefinite for something non-specific and countable.
In this example the speaker is saying they always do this check whenever they visit supermarkets. So, it is 'a' supermarket because there are many of them, but 'the' prices because they mean the specific prices in whichever supermarket they happen to be visiting at the time. The price in one may be different from the price in another.
Consider these examples:
I buy an apple every time I visit the supermarket.
This is because there are many apples and they aren't buying a specific one, and they aren't referring to visiting different supermarkets.
I went to the supermarket and spoke to the manager.
This means a specific supermarket and a specific manager (or the only one the supermarket has).
The definite article can confer "genericity" on its complement.
I like going to the theater.
He is in the hospital.
Saturday is when I go to the supermarket, and the first thing I do is check the milk prices.
Every morning I listen to the weather on the radio and at night I turn on the TV and watch the news.
These are not references to a particular theater, hospital, supermarket, milk prices, weather, radio, TV, or news; the reference is generic in nature. To paraphrase the above:
I enjoy watching plays.
He is an in-patient.
I shop on Saturdays and the first thing I do when I'm there is check how much milk costs.
Every morning I listen to my radio to hear that day's weather and I turn on TV every night to find out what happened that day.
It seems you're following a commonly taught rule of grammar too strictly.
You've probably heard that first you say "a", and after that you say "the". This is only true if both "a" and "the" refer to the same thing.
In your example, "price of milk" is not the same thing as "supermarket", so this rule doesn't apply.
It's bad grammar to say "the supermarket" and then say "a supermarket" if it's the same supermarket. But if it's different nouns, there's no problem.
