1) Given the current bad press, how is an inner city police department to recruit good police officers?
Pay them more (money talks). Provide them with larger working teams (yes, budget increases but teams are able to handle situations in ways individuals and pairs can't). Hire as many minorities of the ethnicity of the respective community that you can (reduces social gap between community and police). Hire people as many people that live in the community they police as you can (reduces social gap between community and police). Build a campaign around a dramatic shift in policing tactics (don't have an answer on tactics as I don't study this, but announcing specific concrete changes, such as how to interact with police etc). Change the uniform, different uniforms for different Police job functions (starts to shift the perspective of police from a monobloc towards individuals). Give them an equivalent of a GI Bill incentive (maybe not for college, but some other post career financial incentive)?
2) What does an inner city war zone turn police officers into?
Veterans. The ones I know that are struggling with the job either are worried about safety (death) or they are on teh extreme opposite where they are going to do whatever it takes to make it out of any particular situation. The majority are likley fine, it's the fringes. Confirmation bias is everywhere in the job of police.
3) What incentive do police officers have to do good work or enter into dangerous or sticky situations?
Noble incentives - the "sheepdog" (people are sheep, criminals are wolves, sheepdogs are the protectors of people). Psychological rush. Whatever reasons they have to join the military.
4) How does a city break out of this cycle of violence?
Persuasion campaign crafted by the leaders of the field (Robert Cialdini for one), A/B tested on a local level. Huge social campaign by the best comedians (who are relevant to that community) who savagely mock the gang lifestyle and gangsters as ridiculous, stupid, pathetic, etc. Economic recovery for low skilled workers. In some cases and forms, link Welfare and social benefits to required public service. Cut off all sources of illegial monetary funds (lock down border to prevent drug inventory coming in). Make anonymous testimony admissable to the court in some way - must work to eliminate the "snitches get stitches" mindset. Close all schools that under perform, open dozens of competing schools in their place with different educational forms - match students with schools based on individual kids learning style.