https://chemistry.stackexchange.com/questions/6212/why-do-the-reactions-of-magnesium-in-steam-and-cold-water-differAccording to this link, the first 'stage' of the reaction between water and a group 2 element (such as magnesium) generally gives a hydroxide. This would be the reaction that requires less energy because it only removes one hydrogen from a water molecule, whereas the second one removes two. However, if given enough energy, water's two hydrogens could be removed and you could get your proposed answer. However, water would only have enough energy to break off its two hydrogens if it was in the form of steam, so only the peroxide would form. Moreover, the reaction would stop after a short time because the peroxide itself is a protective, insoluble layer which halts further reaction. You should just know that water reacts with group 2 metals differently with steam than with water. Also, some group 2s like barium can make peroxides
For your second question, convert 100cm^3 to 0.1dm^3. You can treat the Na in NaCl and Na2CO3 as their own, separate species because it's aqueous. The concentration would be kept the same in both cases. In the end you get:
0.1dm^3 of 0.2 mol dm^-3 Na makes 0.02 moles of Na (n=c*v)
and
0.1dm^3 of 0.2 mol dm^-3 Na2 = 0.1dm^3 of 0.4 mol dm^3 Na (from treating the Na as separate rather than joined up) that makes 0.04 moles of Na (n=c*v)
Adding them together gets
0.06 moles of Na in 0.2dm^3 hence 0.06/0.2 = 0.3 moldm^-3 Na (c=n/v)
Are you doing Edexcel? Exam is tomorrow, scary @_@