What is morality?
Morality is the knowledge that allows you to objectively distinguish right from wrong.
Is morality objective or subjective?
Morality is objective, otherwise it would not exist or make any sense. It would be only a matter of individual preference, like arts or music. If morality was not objective, I wouldn't have any basis to say that my morality is better than yours.
Can moral truth be found through reason?
Yes, but not only reason. Morality to be objective must use all sources of objective knowledge. Objective morality is based on both reason and science. The only morality that makes sense to impose to others and to a whole society is a morality that is objective, a rational-scientific morality.
What is moral for me might not be moral for you. Does that make me immoral? How do we define immorality if morality is just a subjective view?
Descriptive morality is the "morality" you see people follow. But just because they follow a set of rules does not mean that their rules are moral. They can be wrong about their conclusions about morality out of disinformation or ignorance. For instance, people that do not know math well may conclude that their "math" says 2+2=5. But it does not make math subjective, but what they call their "math" in truth is not valid math.
For one person cannibalism could be viewed as objectively moral but for another it could be viewed as immoral. Yes you could say that cannibalism is always immoral but then you are just laying out a rule and expected it to be followed blindly? That does not seem so objective. My point being, you can say x, y, and z are all immoral but no matter what you are laying out a dogma and expect it to be followed. Could we reason that cannibalism is immoral? Sure, but is it immoral because it is a detriment to society or is it immoral for it's own sake? If you argue that it is immoral because it is a detriment to society therefore people shouldn't be cannibals then it falls into dogmatic rule making.
The fuel of morality is empathy. With empathy you can put yourself in the skin of others and notice that they would not like to be killed against their will. Everything you do because "you want", but at the same time ignoring the others will is irrational, and therefore also immoral, by definition. Everything you do against others will is immoral because it is irrational and/or anti-scientific. Using reasoning and science you can discern what actions are moral or immoral. Morality is not a dogma fallen from the sky. It is defined based on the practical consequences of our actions on the factual world.