Every month I try #NixOS again and again, but I don't really move forward. For basic tasks, it seems there exists no simple solution, like:

1. What is the pendant to "apt-cache search <somepackage>" that is FAST?

2. What is the pendant to "apt-cache policy <somepackage>"? I want to know if this package is installed or not, what version is installed and is maybe a newer version available?

3. How to check which packages are upgraded & the version of these packages?