Cheating death and fighting communism: that is how a fellow officer once described our job.  It was meant to be funny, but as time went on it seemed all too true.
I spent more than ten years in law enforcement, all of it on the street in uniform patrol.  I've been a patrol officer, instructor, sergeant and lieutenant. 
Do not report crimes here. Nothing here should be considered legal advice. All opinions are my own.
                             It is impossible for me to tell you where you might like to work.  If you've never lived in a large city, you might love - or hate- it.  Same thing about working in a smaller area.
From my personal experience, I would prefer a smaller department of 50-75 officers if I was starting all over.  Ideally, it would be suburban to rural.  I've worked for a very urban area and for a smaller department in a suburban bordering on rural area.  You get a lot more of the exciting calls in a short amount of time in the urban areas, but you can also burn out much quicker.
The upside to a large agency is you get a lot of opportunity to work in specialized units that you don't have in smaller areas/departments.  For example, a marine unit, aviation unit, SWAT unit, etc.  But smaller areas will sometimes pool resources for multi-jurisdictional units (like SWAT teams formed with officers from several regional departments.)
I'd suggest doing a few ride-alongs with different departments in different areas and get a feel for what things are like. 
                          
If no arrest was made, then there is no arrest record (at least regarding this incident.) Without the victim's cooperation, the officers probably were not able to establish probable cause to make an arrest.
                             Thanks for the compliments.  I am not an ethical expert, but I have always tried to do the right thing.  Teaching me that is one of the many things I thank my father for, and hope to impart to my own children.
If the situation is a casual encounter, and the officer is not involved in some type of enforcement activity (traffic stop, investigating your involvement in a domestic dispute, etc.) I don't see it as a problem.  I see it similar to a UPS driver who is grabbing a soda at a store and talks to someone in the parking lot.  As with all social encounters, discretion and tact are important.
Of course, some departments might have more restrictive policies.  But, I don't see it as being an ethical problem. 
                          
                             I'm sorry, but I'm not clear on the description of the intersection.  My previous answer is based on a standard cross-type intersection.  I'd have to see the intersection and know the laws of your state to give you my opinion (which has no bearing on anything, mind you - for that, contact an attorney.)
But, if you enter the intersection on anything other than a green, then you are likely violating the laws of your state.  If you enter on a green, it is going to depend on the circumstances and how the laws are written. 
                          
Hotel Employee
Can you give guests room upgrades at your sole discretion? 
                                        
                                        
                                             Professional Gamer
What's the longest playing gaming session you've ever had? 
                                        
                                        
                                             Debate Coach
Are presidential debates actually "debates", by the traditional definition? 
                                        
                              You should probably contact a criminal defense lawyer. Most attorneys will talk to you free, and only charge you if you have them perform some action (such as contacting the victim) for you. If you (through your lawyer) act before the company realizes they have been defrauded, there is a possibility you can square things with them before they call law enforcement. A lawyer can help with this.
It depends on how the judge applies the laws of your state. There is no set answer, and much of the judge's decision will be based on the circumstances and history of the child.
On duty generally means he/she is currently being paid by the agency as part of regularly assigned duties. So, it would sound like the officer was off duty.
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