The above is from Knapp's Lie Groups; Beyond an introduction', 2ed, page 397.
Question 1: What is a simple component of a reduced root system? Or, more specifically, given a root system $\Delta$ and orthogonal roots $\alpha, \beta$ with $\alpha \pm \beta \in \Delta$, what is the simple component of the root system containing $\alpha$ and $\beta$?
These terms don't seem to appear in the index of Knapp, and don't seem to appear on Google either. I glanced back at the classification theory of root systems/Cartan matrices/Dynkin diagrams and couldn't get anything
Question 2: Why can't a simple component of a reduced root system have more than two root lengths?
This bound on number of root lengths doesn't seem to hold for root systems of dimension $\geq 3$? But it does seem to be true for two-dimensional root systems?
Blease help me
Question 1: Here Knapp means irreducible component of a root system. As for modules, people sometimes use simple and irreducible as a synonym.
Question 2: This is a well-known fact, see for example this duplicate:
At most two values for the length of the roots in an irreducible root system