What is in-place sorting?
An in-place sorting algorithm uses constant extra space even for producing the output (modifies the given array only). For example, Insertion Sort and Selection Sorts are in-place sorting algorithms and a typical implementation of Merge Sort is not in-place.

What are Internal and External Sorting?
When all data that needs to be sorted cannot be placed in-memory at a time, the sorting is called external sorting. External Sorting is used for massive amount of data. Merge Sort and its variations are typically used for external sorting. Some external storage like hard-disk, CD, etc is used for external storage.
When all data is placed in-memory, then sorting is called internal sorting.

What is stable sorting?

A sorting algorithm is said to be stable if two objects with equal keys appear in the same order in sorted output as they appear in the input unsorted array. Some sorting algorithms are stable by nature like Insertion sort, Merge Sort, Bubble Sort, etc. And some sorting algorithms are not, like Heap Sort, Quick Sort, etc.

However, any given sorting algorithm which is not stable can be modified to be stable. There can be specific ways to make it stable, but in general, any comparison based sorting algorithm which is not stable by nature can be modified to be stable by changing the key comparison operation so that the comparison of two keys considers position as a factor for objects with equal keys.