I'm not aware of any such measures that can be taken without centralising the currency.
Similar to a timestamping server here on Earth (or yes, even an ICANN like construct, but that is centralization, indeed). It will be in the Mars colonists' economic best self-interest to install server(s) that issue a list of timestamp marked credentials - which could be incorporated in each block to verify the mining occurred on Mars.
Raising the money is done with the premine. Beyond that, it doesn't help raise money at all.
Yes it does: the 300k (now 400k) of premined Marscoins are worth nothing at this point (well, on reddit they go for 10-80cents right now). If the incentive is strong enough, more and more fiat currencies will be exchanged for Marscoin driving up the price for Marscoins. That alone will make the initial premining worthwhile and allow MarsOne to actually make use of it. Maybe I should have said "allows to fund activities and make purchases in fiat related to the actual mission roadmap" instead of "raise money".
Keep in mind that the difficulty needs to be high enough to make it resistant to attacks...
See the above answer regarding the credentials incorporated into each block by a (network) of security servers that could form the backbone of a Martian internet.
Let me know what needs to be done, in your opinion, to convince you of Marscoin? Curious!