I think it is awesome that you are interested in engineering. Classes you can take are in math(alegbra, calculus) and science (physics, chemistry). There are many different engineering disciplines I will list only a few of the main ones here ( chemical, mechanical, electrical, computer, industrial, civil). This website can give you a little more information on the different types http://www.ic.sunysb.edu/Stu/hnaseer/photo.htm . Also depending on the type of engineering discipline you would like to go into you see if your school offers classes in computers, electronics, cad design, mechanical design etc.
To answer your second question about body modifications, it depends on where you work and your manager. Most jobs in corporate america for example might require you to cover up your tattoos or take out your nose ring because of the company culture. In manufacturing settings you might be ok but they make ask you to be careful when working with certain equipment on the floor. But many people are always happy to share their policies with you.
I hope this helps let me know if you have anymore questions.