Side note for completeness: You cannot make this conclusion the other way around, that if between two features, the correlation = 0, those features would be independent. This would not be true in general.
This does not work since only the linear dependency is assessed but still other kind of dependencies are possible, see also this viz e.g. if you have a circular pattern / dependency:
- https://upload.wikimedia.org/wikipedia/commons/thumb/d/d4/Correlation_examples2.svg/1200px-Correlation_examples2.svg.png
- Correlation - Wikipedia
I would really recommend to visualise your data! This helps often to find patterns or see dependencies.
Best regards
Christian