Why are the two 才s used in 很多小朋友以为长大了以后才能自由自在。他们不知道，他们才是最自由自在的? The page I followed on Instagram uploaded a picture complete with its caption that says :


  很多小朋友以为长大了以后才能自由自在。他们不知道，他们才是最自由自在的。


They also provide this translation :


  Many children think they can 自由自在 after they grow up. They don't know that actually, they are the one who is the most 自由自在.


What I want to ask is, why do they use 才能 instead of 能? Isn't 才能 a noun? (Cmiiw).

Next, why do they put 才 between 他们 and 是? What does 才 mean here? Does it refer to the word "actually" in the translation? But doesn't 才mean "ability/talent"?
才 is ability, talent when used as a noun.

In your examples, however, it's used as adverb. The first 才 in 很多小朋友以为长大了以后才能自由自在 is used as the sense 1 below and the second 才 in 他们不知道，他们才是最自由自在的 is the sense 2 below.


  
  表示只有在某种条件下，或由于某种原因、目的，然后怎么样。
  由于抢救及时，这批图书才保存了下来。
  强调确定的语气。多与语助词“呢”连用。