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!