The statement, "Recursion is always better than iteration" is false. There are cases when either one is preferable over the other.
It's difficult to give you a decisive answer over which type of algorithm to use because it depends on the particular case. For example, the common textbook recursion case of the Fibonacci sequence is incredibly inefficient using recursion, so it's better to use iteration in that case. Conversely, traversing a tree can be implemented more efficiently using recursion.
To answer your second question, yes, any iterative algorithm can be implemented using recursion and vice-versa.
