Best of luck starting a career in research. Regarding math, bear in mind that different areas of work will have differing requirements in the amount and kind of mathematics involved. An archaeologist will need to be comfortable with basic, high-school level math, while an astrophysicist will need a good deal of advanced math. Look at the course catalog for the school you are interested in; it will list the required courses for each major, including the math courses. Individual course descriptions typically list the pre-requirements for the course. For most of the areas you are interested in, a research career will necessitate obtaining an advanced post-graduate degree -- looking at the pre-requirements for some of the graduate courses offered in your area might also prove useful. If a research career begins to look too intimidating, bear in mind that rewarding work may be available assisting in research. For example, I am an astronomer, and when I make observations I often rely on skilled telescope operators to actually control the telescope I am using. The operators jobs put them in the middle of astronomical work while not requiring the advanced mathematical skills needed to master physics. I'm sure similar jobs exist in most of the other fields of work that you expressed an interest in.
I think it quite admirable that you are willing to make an effort to start a new career path at an age where many would think it impossible. Be reassured, it is not impossible, I have seen successful graduate students who also embarked on their scientific careers later in their lives than the "normal" path.