Nilearn atlases coordinates and labels

It is possible to grab the coordinates based on atlases as the input. Please have a look at this example:
https://nilearn.github.io/auto_examples/03_connectivity/plot_atlas_comparison.html#sphx-glr-auto-examples-03-connectivity-plot-atlas-comparison-py
The function find_parcellation_cut_coords does that.

To find labels on BASC. Follow this thread this may give some insights.

For Power atlas, what we return are the MNI coordinates. Following Power et al 2011 paper or Neurosynth can give you the labels of these coordinates ?

Hope this helps.