Learn Finnish: Terveellinen ravinto sisältää aina ainakin vähän kuitua. - Healthy nutrition always contains at least a little fiber.

Not naturally. Vähintään is strictly used for measurable numbers or exact quantities (like vähintään viisi grammaa - at least five grams). Ainakin is much better here because it pairs with an abstract, subjective quantity like vähän (a little), expressing a minimum expectation rather than a mathematical limit.

Is it normal to stack three adverbs like aina ainakin vähän right next to each other?

Yes, it is very common in Finnish. The word order flows from the most general concept to the most specific. Here, the time frequency aina (always) comes first. Then, the scalar adverb ainakin (at least) must sit immediately before the quantity vähän (a little) because it directly modifies it.

Why is kuitua in the partitive case?

This is a quick refresher: quantity words like vähän (a little) or paljon (a lot) always force the noun following them into the partitive case. Since kuitu (fiber) is an uncountable mass noun, it takes the partitive ending -a.

Why use ravinto instead of the more common word ruoka for 'food'?