1. How will a tattoo look when the underlying skin is brown? I mean, will it be like mixing 2 colors with each other, or will the ink overpower the spot's pigment?
No, it's not mixing colors. Your artist should create the design with this in mind.
2. I know that tattooing on high-friction, high-moisture areas (exactly like mine) isn't the brightest idea, because the tattoo might fade away quick. Is it true?
I've never heard of under arm tattoos fading quickly. It's not like it's on your foot and you're walking on the skin all day.
If it is true, how come the "natural" brown pigmentation I have hasn't faded away?
It's not true.
Are tattoo pigments and my pigments residing on different layers of the skin?
Ink goes into the dermis or second layer of skin just below the epidermis. Where is your pigment?
3. Obviously my skin is more sensitive than others'. Is there any way to assess the consequences of having a tattoo?
Can I be allergic to the ink?
Actual allergies are extremely rare. Some people are more sensitive to some colors, but if you do the research, you'll find that few medically documented cases of people being allergic to ink.
Can the tattoos cause inflammation like the deodorants did?
It's possible, but if your doctors can't answer the question, it's unlikely a tattoo artist could.
I read that most inks contain some nasty metals and unfriendly materials that will surely irritate my skin.
No, No, No, No, No. Millions of people get tattoos and only a tiny percent every have problems. If the inks were so toxic, there would be a lot of people with problems.
But maybe are there natural pigments or anything less harmful that I could tolerate?
You don't know until you get the tattoo. Tattooing a tiny spot to "test" the ink doesn't really do anything.
4. Since the area is close to the lymph nodes, do you think that the ink can somehow diffuse to them and cause unwanted effects?
Plenty of people get tattoos next to and over the lymph nodes. I wouldn't worry about that.
Or am I too paranoid?
Better to ask the questions BEFORE you get a tattoo than after. There is nothing wrong with doing thorough research before deciding if you want to go ahead with the tattoo.