The Signal client is open-source. Portions of the Signal server are not open-source. In particular, the portions written by the NSA. (joke!) It’s not very clear why. But it wouldn’t really matter since Open Whisper Systems runs all the servers and could change the running code to some extent. This brings up another issue with Signal, besides the fact that it runs on iOS/Android. Here we have Privacy by Policy - their claim that they only keep limited metadata - that is difficult to work around. With OTR, I can simultaneously have 20 accounts on 20 different XMPP servers on 20 Tor circuits - not sure if that’s possible with Signal.
Google Play services are used as a convenient delivery mechanism and most importantly, for Google Cloud Messaging (GCM) - the notification engine. AFAIK it is possible to install Signal on a rooted phone using F-Droid and also possible to avoid GCM by installing GmsCore. Signal also accepts registrations coming from VOIP numbers, which should open up the program to Android emulators. [Still too many unknowns with Android and Signal servers for my paranoia.]
@HulaHoop pieces of shit noted. Will update OP and add task to my wiki list. Also, any comments regarding the little bit about hosting your own XMPP server? Obviously, it’s better for you than your contacts but any obvious deficiencies? Is there inter-server leakage when all activity (registration and messaging) occurs on one server? It could be a decent workaround when a paranoid Whonix user needs to communicate with OTR-only contacts…