It doesn't matter that they're superlatives. In all of these examples, the superlatives don't have articles, because they're just adjectives or adverbs. If they weren't superlative, they still wouldn't have articles, because English articles only go on noun phrases, not adjectives.
"My good friend": my is a determiner, which takes the place of the article on friend.
"He runs fast": fast is an adverb here, and so is fastest.
"Tea is good when served ...", "I know what is good for you", "OK, if you think that's good", "It was a perfect example of all that's good and admirable": all of these have a verb attributing an adjective to a noun. Nothing changes when the adjective becomes superlative.
There are a few constructs where a superlative takes an article. The most common is that it can be used as a noun. When it's a noun, it takes an article (or other determiner) just like any other noun. For example:
- "Of all animals living or dead, the biggest is the blue whale."
- "I like all kitties, from the cutest to the most bedraggled!"
- "This poem is not my best.": best is a noun here, so it would usually have an article, but in this sentence it has my instead.
But in all of your examples, the superlatives are simply adjectives or adverbs, with nothing tricky going on.