Questions about Randomized Median algorithm?
Let's start with your second question. A random running time is a running time which is a random variables. As a simple example, consider an algorithm which tosses a fair coin until it come up heads. The running time is a random variable whose distribution is, roughly speaking, geometric. This is not so different from the randomized median algorithm: every run of the median algorithm is like a coin toss, and you iterate running it until it comes up "heads" (succeeds).

Now, for the name iterative algorithm. Here is the algorithm you describe:

repeat
  run Algorithm 3.1
until the algorithm succeeds


This is the epitome of iteration – the algorithm consists of a single loop.

You write


  In order to get an iterative algorithm, then the algorithm must call itself and must have a logarithmic running time.


I'm not really sure why you think that an iterative algorithm should call itself. Indeed, algorithms calling themselves are usually known as recursive algorithms. (As an aside, an iteration of the form considered here is a special case of recursion known as tail recursion.)

Also, I'm not really sure why the algorithm should have a logarithmic running time. The standard algorithm for summing an array is iterative and runs in linear time.