Never a Best Response and Belief
Your understanding is mostly correct, but the following sentence is not: 


  in simple games, you often face with a situation where one of the pure strategies a player might have, say Column L of player 2, never gets underlined when you work out which ones for Player 2 is BR.


Consider the following counterexample: 
\begin{array}{|c|c|c|c|}
\hline
 &amp;L&amp;C&amp;R\\\hline
U&amp;1,3&amp;3,4&amp;3,0\\\hline
M&amp;2,3&amp;0,1&amp;0,4\\\hline
D&amp;0,0&amp;1,2&amp;2,1\\\hline
\end{array}
In this game, $L$ is never a BR to any of player 1's pure strategies. However, if player 2 believes player 1 will play a mixed strategy that assigns $\frac12$ probability to $U$, $\frac12$ to $M$ and $0$ to $D$, then $L$ becomes a BR.