Colons and dashes

A dash can be avoided by recasting the sentence slightly, especially if you are using too few or too many words to express an idea.  You may also want to break down a wordy, multi-idea sentence into two sentences.  I would say that your use of the colon in your first sentence is correct, but you could also replace it with a comma.

You could also say, "I want to become an archeologist, someone who opens closed doors and works closely with the origins of life."

"What fascinates me most about science, the most interesting of disciplines, is the unknown.  I want to explore those areas where everything doesn't yet fit together."  (Or the same wording with a semicolon after "unknown" instead of a period.)

I think it's a good idea to avoid too much use of the dash and to replace it with more precise punctuation or wording.

Others here who are better writers than I am might give you more effective ways to rewrite your examples.

David offers some interesting suggestions, but he is wrong on several points.

(1) The use of the colon is wrong. Colons are used to introduce lists or block quotations. A comma is the proper punctuation:

"I want to become an archeologist, opening closed doors and working closely with the origins of life."

(2) Although David's suggestion is good, you do not need to recast the sentence to eliminate the em-dash. The em-dash is an emphatic substitute for a comma. It should only be placed where a comma would occur. You can replace the em-dash with a comma:

"What fascinates me most about science is everything unknown about this most interesting of disciplines, areas where everything doesn't fit together."