Can I use these interchangeably?
You can hang around if you'd like..
You can stick around if you'd like.

Question

Answer

Both have similar meanings, but they have different connotations.

By saying 'stick around' you are giving the person the right to stay.

by saying 'hang around' you are also allowing the person to stay, but at the same time you are giving permission to move around with freedom.

Answer

Both expressions are widely understood to have the same meaning. "Hang around" is more common.

Answer

Yes they are both the same.