These are great questions!
Generally, I do not think that targeting exercise to your heart rate is very important for the typical person who is trying to exercise to maintain general fitness/health and/or lose weight.
In any case, there is a recent study that suggests that we should calculate women's "predicted maximum heart rate" differently from men's - using a slightly different formula. Using that formula of 206 - (0.88)(age), yours is about 171. This suggests that the average woman without heart disease should be able to reach a heart rate in this range with exercise. So 165 shouldn't be a problem for you.
Then there's the whole "fat burning" question. I would try to think about it more simply. Exercise for more intensity and for a longer time, and you will achieve a greater benefit. However, there is some data that suggests that brief spurts of high intensity exercise interspersed with a slower steady rate could actually result in more weight loss than a longer period of moderate exercise. So you might consider some interval training as part of your regimen.
Best of luck! Check out www.theflexdiet.com for some other fun ideas.