> Also, a Mars colony that could survive indefinitely if the Earth is wiped out is almost certainly impossible, given the extreme conditions on Mars' surface.
Let's say you have a Martian colony of 100,000 people. It is self-sufficient in basic goods but still relies on imports from Earth for many advanced goods. Something terrible happens, and imports from Earth are no longer possible. Those 100,000 people have a choice – find a way to make do with what they have, or die. I don't think we should underestimate human ingenuity in such circumstances. They'll lose access to a lot of highly advanced goods – for example, they probably won't have their own leading-edge semiconductor fabs – but they may be able to survive without them, using more basic goods to take their place.
> Then, you'll also be missing nitrogen
The atmosphere of Mars is around 2.8% nitrogen. There are likely to also be nitrate minerals in the Martian soil and rock.
> Oxygen will be in short supply
Mars' atmosphere is 95% CO2. You can extract oxygen from CO2 by electrolysis. The MOXIE experiment on Perseverance has demonstrated this.
> and solar winds are constantly stripping away Mars' atmosphere
On human timescales (decades to millennia), Martian atmosphere lost to space isn't significant.
> Also, the cost of building a self sustaining colony on Mars is well above the GDP of the world many times over
I think Musk is going to try to establish a settlement on Mars, initially with tens of people, then hundreds, then thousands. And becoming fully self-sustaining is going to be their long-term goal. But I don't think actual full self-sustaining status is going to be achieved for several centuries.