Learn Spanish (Spain): Afortunadamente, tus reflejos son rápidos.

Both express relief, but they function differently in a sentence. Afortunadamente is an adverb meaning "fortunately" that modifies the whole sentence. Menos mal que (thank goodness that) acts as a conjunction and must be followed by a clause with a conjugated verb in the indicative. You could easily swap them here and say: Menos mal que tus reflejos son rápidos.

Why do we use son (from ser) instead of están (from estar) for being quick here?

We use ser because having quick reflexes is being treated as an inherent characteristic or defining physical trait of the person. If you wanted to emphasize that someone's reflexes were unusually fast just in this specific moment (maybe they drank a lot of coffee), you could technically use estar, but reflex speed is generally treated as a permanent attribute.

Is afortunadamente common in everyday spoken Spanish in Spain?

It is perfectly understood but sounds slightly formal or written. In casual spoken Spanish from Spain, people are much more likely to say menos mal or por suerte (luckily) to express this exact same feeling of relief.

Does the word reflejos have any other meanings besides physical reflexes?

Yes! Besides physical body reflexes, reflejos is also the plural noun for "reflections" (like light reflecting off a mirror or water) and is the standard word for "highlights" in someone's hair.