If I retire at 65, my wife will only be 60. Can she continue to work and receive her full pay, or will I be penalized if she makes over 15000. Are our incomes looked at seperately if one retires and the other works.
No, your wife's earnings would not affect your Social Security retirement benefits. Only your own earned income (i.e. wages and self-employment earnings) counts toward Social Security's earnings test (https://www.ssa.gov/planners/retire/whileworking2.html).
Before filing, though, you may want to consider using the maximization software available on this website to explore your options and determine the best filing strategy for you and your wife.