In terms of future events, the present continuous indicates an event that will happen in the near future, so
"A spaceship with a human crew is landing on Mars tomorrow"
works, but
"Sometime in the next twenty-five years, a spaceship is landing on
Mars"
is just too far removed from the present.
Remember that the PrC connects to the present - if you say they are landing tomorrow, we can imagine that right now, in the present, they are making the preparations towards performing and completing that near-future action (note: "they are landing tomorrow" does not in itself mean "they are preparing now" - the present state is simply implied).
When you say "In the next 25 years" (and especially with the vague "sometime"), the point of completion is entirely in the future - so far in the future, that it is difficult to imagine the connection to the present at all.
Of course, PrC can be used for a longer action in the present that will have consequences in the future. In this case, you would say
"They are preparing to send a spaceship to Mars",
even though the actual sending might be 25 years in the future.
As for "the sun is burning forever", "forever" includes the present of course, but it also points way, way into the future - and of course indicates that the action will never be completed. "I am studying nursing" works because completion will occur in the near future, and there will be an effect of the present action in the near future.
You can say "The sun is burning today", but of course the burning of the sun now does not indicate its state of burning in the distant future (grammatically speaking).
EDIT: As Nico points out, if you want to use "keep", this will not work with PrC: one would not formally say "The sun is keeping shining".
"I will fix breakfast" indicates that I will (more or less) definitely produce a meal, though possibly not until after my mid-morning nap. "I am going to fix breakfast" indicates that I fully intend to cook something, probably fairly soon, though I may need to trim my beard, polish my nails, and read the newspaper first, and there's a risk I'll end up forgetting about the cooking task.
Both forms have potential (dependent on context and tone) to be "weasel words", though "will" (especially if emphasized) conveys more determination while "going to" indicates a bit more urgency.
Best Answer
It's basically identical, yes. The phrase suggests that the thing being done is slightly difficult or laborious in some way, or perhaps that is has previously been delayed for some reason, but it's very subtle. This is likely to be spoken English, not written.