Hi, I thank you in advance for your collaboration. I am really new in this area and I have some doubts about the analysis of the results that I have obtained so far.

To evaluate the alpha diversity of my samples, I used the Shannon and Simpson indices. For the Shannon index I obtained values between 3.98 and 7.03, and for the Simpson index between 0.95 and 0.99. I understand that the values I obtained for the Shannon index indicate that there is a high richness and homogeneity in the samples. On the other hand, the Simpson index tells me basically the same thing (high richness, but no species dominance). Is that analysis correct? Is the Simpson index calculated by Qiime2 the "normal" one and not the Simpson inverse?

Yes! The 0.95 and 0.99 Simpson index are the chance of drawing two different features from your sample, and not the inverse Simpson index.

Almost... Both Shannon and Simpson measure a composite of richness and evenness. This matches your observation: one sample has higher alpha diversity (0.99 and 7.03) and one sample is slightly lower (3.98 and 0.95).

If you want to measure richness and evenness separately, check out this list of alpha metrics:

P.S. You are making good progress and asking all the right questions!