Booleoans is sometimes a pain...... if you making something circular, try using nurbs curves and loft them, once you get the depth and shapes you want.... then you can than convert them to polys and make them one object.
If you want to move multiple ojbects you have to group all the objects together. Once grouped, pick the top node in the hypergrape and than you can move all the objects together.
I am enough of an artist to draw freely upon my imagination, knowledge is limited, imagination encircles the world. (Albert Einstein)
https://www.artstation.com/kurtb