I don't have access to the diagram you're referring to but hopefully this will still help.
1. I think you're referring to variance minimising portfolios:
When rho = -1 we have two perfectly negatively correlated holdings. If you wanted to minimise the risk of your portfolio then you would hold an equal weighting in the two, S1 and S2. This is because as one increases, the other decreases. For example, if S1 increases by 10% then S2 would decrease by 10% (perfectly correlated). If you held equal weight in the two then the increase and decrease would cancel each other out each time leaving no risk.
Similarly, if rho = 1 we have perfectly positively correlated holdings. If you want to minimise risk then you can again get to zero risk. Considering S1 and S2 as the holdings again: if S1 were to increase by 10% you know that S2 will increase by 10%. Therefore, if you had shorted S2 then the gain from S1 would be offset by the 'loss' due to your negative position in S2. If you are holding the same positive quantity in S1 as your negative quantity in S2 then any gains/losses will always cancel each other out, leading to zero risk.
2. Please post the diagram (the copyright shouldn't be an issue for this).