What you describe is entirely consistent with K date Lugers. The reason for the use of the S on parts is unknown, at least to me. There are some guns known with an "a" suffix indicating that over 10,000 were made; some estimates are about 10.500. (German military serial numbering started each year with 1, went to 9999, then 1a to 9999a, 1b to 9999b, and so on.)
The "K" instead of the actual date (1934) was used in an attempt to conceal increased military production from Allied Versailles treaty inspectors, who were still in Germany at that time. (The letter "G" was used in 1935, but in 1936 the pretense was dropped and the real date used.)
Original magazines have the aluminum bottom with the full serial number. The extra magazine will have a "+" mark.
Jim
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