Here's my interpretation:
1. When I grow up I ______________ a doctor. I've always wanted to be a doctor – that's why science is my favourite subject.
A. am going to be
B. will be
---- "am going to be" is the better choice here since it illustrates intent and planning. "will be" shows certainty, which can't be guaranteed at this point
2. Fifty years from now, everyone will be using bicycles. The world _____________ out of oil and everyone will be much healthier.
A. is going to run
B.will have run
---- "will have run" shows that oil has run out, which I think was the intent of the writer- fifty years from now, the world will have run out of oil.
3. This time next week, most of us _______________ in exactly the same seats, doing another test like this one.
A. are going to sit
B. will be sitting
"are going to sit" illustrates planning, that most of you are planning to sit in the same seats you are sitting in today.
"will be sitting" illustrates fact, You will be sitting in the same seats.
Both are OK, depending on intent. I like B better, since I don't think the writer wanted to emphasize planning on the part of the test-takers, but rather to state what will happen. But I could be wrong on that.