Trying to understand the contradiction in the data of Proust/Dalton/Berzelius vs Gay-Lussac
In regards to your first question, I would think that Dalton would have a sense of the molecules' formulas based on the information at hand. Not only did Dalton have the mass ratios for these compounds, but he had also developed a measure of the relative mass of the atoms, as shown in your first document. Given this information, it would not have been difficult to compute that there were $\sim2$ atoms of nitrogen for every one of oxygen in nitrous oxide, nitric oxide was one to one, etc.

In regards to your second question, I think you are misinterpreting the contradiction. The authors proposal for the reactions was that if the compound formed was $\ce{N2O}$, it should only form one volume, since it should only form as much volume as there was volume of $\ce{O}$ originally. This is because there can only be as many molecules formed as there were atoms of the limiting reactant. The two volumes of $\ce{N2O}$ that are actually produced runs counter to this, as it would seem to require having $2$ volumes of $\ce{O}$ to start with.  

For all the reactions, the products and reactants were related by whole number ratios, but not the same ratios suggested by their predicted molecular formulas.