Hi,
the standard procedure for most of the corporate (endpoint) customers is to contact either their re-seller or our support (support.avast.com). However if you are fine with this forum feel free to post you issues at this forum.
Q1 : My real question is It seems that whenever I deploy one or two machines via the remote push, all of the ones that are already there and in groups get moved to the unmanaged group. Am I missing a setting that would prevent this from happening or is it normal.
A1 : I expect that you are using the "wizard" not a Job for the deployment, right? And the wizard is only for the "first time use". It does exxactly what you said. It puts all "computers that you haven't choose as managed" to unmanaged group.