chocoholic, re: curdling, sounds like you are using the right sugar and milk, be sure to limit heat as well- bring the caramel up to the right temp, turning down the heat as you approach the target zone so as not to go over. Then pull it off the heat immediately and cool quickly, perhaps even dip the pan into a bowl or basin of cold tap water to lower the heat. I point this out because you mentioned that you kept cooking it- more than was required? Or just to bring it to the right temp?
Don’t worry about what others’ pictures looked like- maybe they snapped them before the mixture came all the way up to temp, or resolution was low, etc. I often make cakes using frozen dairy that has separated and they turn out just fine, cakes have enough emulsifiers in the formula to take cake of that.
That said, if your curdled lumps are huge- pea sized, for instance- then cool the mixture, and once it is cool blitz in blender if you like.
If it helps, remember that curdling isn’t always bad and in most cases doesn’t signify that anything is wrong or unsafe to eat. If you’re making ricotta, curdling is good; if you’re making custard, it isn’t. It just means that the proteins have been denatured by the combination of acid and heat.
re: sizing up your recipe, a butter cake needs a little more strength to hold itself up in a larger pan- just like a bridge needs more strength to span a wider river than a narrow one, a cake needs more strength to hold up between the side of the pan when they are farther apart. One easy way to increase strength in a butter cake batter is to reduce leavening, so that is why FRESHKID said not to scale up the leavening. Sounds perfectly reasonable to me