1) It is possible to print money in a 51% attack if other users don't have the full history. 51% Attacker outruns the whole chain by more than the month that everyone does store, so that NO-ONE has the history. Then you can do what you like. not very likely I agree.. (Outrunning a month with 51% takes Years)
Oh really?
I don't believe that. In particular, I do not believe that he could spend my coins in case that was included in the subset of things "that he liked to do".
Furthermore, it is also not true that outrunning a month with 51% of the total hash power takes years. If prepared correctly (and not script kiddy style) it takes exactly one month + a few minutes.
Think of it this way. We both keep tossing coins, every day each of us tosses once and we count the number of heads that each of us accumulates.
So when will I, for the first time after a month, have more heads than you?
Well, after one month, on average each of us is expected to have 15 heads. But when will I have more heads than you? It isn't that hard:
- Within 1 month and 1 day: I have more heads than you with 50% chance
- Within 1 month and 2 days: same story! Every other day I have (on average) a new 50% chance to revert the full month, considering that the numbers of heads we both got will converge towards the same value over time. You just need to be longer once for a very brief period of time to pull it off.
When you look at the maths, your advantage might be even higher with 51% (as opposed to 49%).
Since it's not the "longest" chain (as frequently claimed) but the chain with the most work that survives, you will have a lower difficulty drop on retargets than the 49% of the network, meaning that your chain might be heavier without you mining noticably less blocks. So even when your chain is not longer, it might still win! I am just too tired to do the math now.