Interesting questions, indeed. As father of three pretty daughters, ages 13 (today), 14, and 8, my answers are heavily colored by parental concerns.

At what age is a person sexually considered an adult?
The legal assumption is that a person below a certain age lacks the experience and maturity to make a rational choice, even if they are making a conscious choice. Maturity depends (as others have said) on the individual; experience depends on environment. A 20-yo virginal woman, protected from all carnal knowledge, could very well be "raped" in her nuptual bed, given her lack of knowledge; a 13-yo girl who "voluntarily" prostitutes herself under economic duress is equally raped. But a well-informed 14-yo who deliberately seduces a man (or woman) with lies and without pressure -- that is not rape.

Sexual law is a nebulous area, difficult to define in absolute terms. All laws are open to interpretation, but it is far easier to enforce something concrete (stop for red lights) than is is to define "consent" in sexual relations.

In a truly mature society, we could handle each situation individually and with great deliberation; alas, humans are still quite reactive and prone to unthinking fundamentalism. I'd be a libertarian if I trusted people -- but I continue to see signs that we need some sort of common, clearly-deined rules.

Witness Montana's attempt at eliminating speed limits on highways, under tha assumption that people would show common sense. Accident rates (which sometimes killed the innocent) skyrocketed as idiots raced across the plains. Montana has since reinstituted speed limits. I hesitate to think what would happen if sexual laws were left open to "common sense"... ;}

At what age is a person mentally considered an adult?
Too variable to define, and often situational. I might be an "adult" in some circumstances, but not in others. I certainly know that my eldest daughter sometimes shows signs of being more mature than her father on certain topics...

How do geographic, economic and societal stresses and influences affect your decision?
Should an age of consent apply to age of marital conset as well? If it should, how should the age of marital consent be affected?
In my opinion, marriage is a legal union that implies a sexual component. Marriage is a commitment, something that should be honored regardless of the ages and sexes of the individuals involved. Like sex, the commitment of marriage is something that different people are ready for at different ages.

If a worldwide age of consent were reached, how should it legally be enforced? Should there be exceptions in cases of parental approval? Should there be an exception if both parties are under the legal age of consent?
It won't happen in our lifetimes without a global, totalitarian government. Societies differ far too much for any common law to be applied voluntarily, worldwide.

Given technological advances and new science, are today's laws adequate to deal with underage sexuality? What could be done to further improve the laws governing age of consent?
Technology has nothing to do with it. The problem isn't underage sexuality -- it is a culture that devalues commitment and promotes gratuitous pleasure without regard for consequences. Irresponsible underage sex is a symptom, not the disease.

Finally, in cases of underage sex leading to pregnancy, what should be the determined outcome of the fetus? Should all fetuses carried by illegally impregnated mothers be immediately terminated? Should the underage mother's parents decide what is best for the fetus? Should the underage mother be given a say in the matter? Whose responsibility should it be to raise the baby, if the fetus is allowed to go to term?
This topic will take us far from the original premise -- and another set of questions that have no absolute answers.