Your premise for Type 1 is correct, however you seem to have misunderstood Type 2: It is no problem to continue mixing the butter-sugar-egg mixture, but as soon as the flour is added, the gluten starts to develop and you should just mix until combined.
For Type 2, creaming the butter and sugar helps to incorporate a lot of air into the mixture, resulting in ...
It's not a problem to continue mixing it, in fact mixing is not only okay but required
You seem to have misunderstood something. It is as much or as little a problem as with the other type of cake. The more you mix it after full incorporation, the worse your cake texture will be. You have probably overestimated the effect of overmixing in the first type (...
The recipe looks fine. I suspect that you are incorporating too much air into the batter when you are mixing. Try:
Mixing less - shorter time/slower speed and/or use a regular beater rather than a whisk
pouring the batter then giving the tin a good hard tap down on the bench - this will make large bubbles rise to the top and come out of the batter.
Yes, cakes will go stale faster in the refrigerator, as will most baked goods with a high starch content.
Staling (as discussed over at Serious Eats) has to do with starch recrystallizing. As Harold McGee explains (pp. 541-542 of On Food and Cooking):
Staling is now understood to be a manifestation of starch retrogradation, the recrystallization, water ...
My mother (a retired Irish Home Economics teacher!) says that a true sponge cake contains no fat (ie. no butter - butter in the recipe makes a 'butter sandwich cake', not a sponge). For her sponge, she separates the egg whites and yolks, beats them separately, and uses only the egg whites as the raising agent - and her sponges are beautiful!