A - the AOR is generic. In some economic class streams (FSW, PNP) it does matter whether you quit or change employers. But it has absolutely no bearing on a CEC application. Go ahead and inform them if you want to, it will not matter one whit.
B- The only reason CIC might ask for more paperwork is if something isn't right with your application. For CEC applications, the only work experience that matters is what you did before you applied. I realize that part of your experience is in January 2014, but since most of your experience is on the 2013 T4/NOA, I don't think you have anything to worry about.
C- whenever an employee quits or is terminated, the employer is REQUIRED BY LAW to (a) prepare an ROE on paper and GIVE YOU A COPY within 5 days, or (b) submit an ROE electronically to Service Canada, If your employer submits it electronically, you can download it from the Service Canada website. If your employer refuses to do this, you can ask Service Canada for help.