Are there dangers from making alcohol by fermenting sugar with yeast?

No danger. Fermenting sugar with yeast will not yield methanol. You will be drinking ethanol, the only danger is based on quantity, if you drink more than you should...you know the results. You will not need to test the result to see if it is methanol, it won't be. Finally after filtering you can still let it age without a "separation fear". I used to make my own beer and the couple weeks of aging after the first few filtering steps is what made it so smooth and drinkable.