Is standard Quicksort stable?
No.
Swapping elements across long distances (like partition does) changes relative order of equal keys.
You need to sort an array that is "almost sorted" (only a few elements out of place). Which algorithm is likely fastest?
Insertion Sort.
It runs in O(n) for nearly sorted data.
Quicksort (with first element pivot) would actually be O(n^2)! Merge sort is always O(n log n).
There exists a pivot selection strategy that guarantees O(n) worst-case time for Selection. Is it used in practice?
Mostly No.
The constant factor is very high. Randomized QuickSelect is usually faster.