For question 1, I don't think you're supposed to subscript the v's. That is, all the vectors in S look like scalar multiples of a single, given vector v, just with different multiples in the interval [0,10]. And here, perhaps, you can see what fails in terms of the vector space axioms.
For question 2, I would think of the problem geometrically. You have two equations there. Geometrically, what shape does each equation represent separately? And if they both have to be true, what sort of shape is described by the simultaneous equations?