1. Even though both selection sort and insertion sort are
both O(n^2) in the worst and average cases, in the best case
insertion sort is O(n).

The best case for insertion sort is when the data is in sorted 
order.  When the data is sorted, the amount of work to "insert" 
each element into its correct spot in the already sorted portion 
of the list is just constant.

Even if a few of the items in the list are not in order, for all 
of the other items in the list, we will still have just a 
constant amount of time, so if the list is mostly sorted insertion
sort will still be qite fast.  On the other hand, selection sort
always takes the same amount of time regardless of input.

2. Big-O notation just described how the run-time of an algorithm
will grow over time.  In the limit (or for very large input) A will
be faster than B.  However, there could still be some inputs where A
is faster than B.

Take for example insertion sort.  It is an O(n^2) algorithm, however,
on some inputs, it runs quite quickly.