Hi Richard

Q4 is presumptive - that Community Policing -improves- public perceptions.  (1) How do you know that this is a general rule? (2) If this is a general rule and you're asking 'how?' then you've already provided the policy implications, again generally speaking, of the ensuing investigation into the other three Qs (i.e. more community policing mitigates any negative outcomes / differences discovered in the investigation).  So I can generally predict your conclusions prior to any findings or analysis of findings, which is more community policing!

I recommend you zero in on an overarching research question (which you can then subdivide) - I don't see one.  You're also potentially conflating Sir Robert Peel's statistically-driven utilitarian policing with community policing.  The two are quite dissimilar: Peelian policing culminated with 'Professional Policing' based upon visible deterrence (random patrol), rapid response to calls for service, and reactive investigations.  CP requires partnerships between communities and police to (a) identify problems underpinning criminal activity (b) try to solve those problems by leveraging community resources - not necessarily through police enforcement of law, and (c ) reflect upon the effectiveness of how the identified problems were addressed.  There is obviously a great deal of literature on problem oriented policing, SARA, CAPRA, etc.  Community policing is not deterrence-based, nor is it driven by crime-trend statistics (at least not per se).  Lastly, I would urge you read-up on NIM, Intelligence-Led Policing (a UK developed export for global adoption - thank you /sarc), and of course here is the plug for one of my papers - see Deukmedjian (2013) 'Making sense of neoliberal securitization in urban policing and surveillance,' Canadian Review of Sociology, 50(1).    

Hope this helps.

JD