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Hi Sonja,
as to the sort of test - the post-hoc tests are based on the standardized mean rank differences of the two samples. The exact formula is provided in the SPSS help under "Pairwise Multiple Comparisons (nonparametric tests algorithms)".
The column labeled "Sig." lists the uncorrected significance values. As you noted correctly, you should not use these as the multiple comparisons lead to an alpha cumulation. The column labeled "Adj. Sig" are the Bonferroni adjusted significance labels, that are calculated as p*K*(K−1)/2 with p as the uncorrected significance level and K as the number of comparisons. Use these values for you analysis.
Timo