I sweeten Asian cooking with (coconut?) palm sugar or, if Indian cooking, dark chocolate. I saw that tip on a TV cooking programme and it stuck with me. Works well.
I do eat loads of white sugar I'm sure: in things I buy like cakes, jams and yoghurts, so I'm not claiming to not eat the stuff - it just happens I don't use any as a cooking ingredient.
Nope. Palm sugar is refined coconut tree sap. Coconut sugar has a brown color to it and tastes like slightly burnt sugar. Palm sugar looks the same but has a slight mineral flavor leaning towards iron, much like molasses. Palm sugar is also known as coconut palm sugar. Coconut sugar is simply coconut sugar made from refined coconut mush. Both are fine in coffee with steamed milk if not a little too indulgent.
Both are good in chocolate cake. Take a bit of the white sugar out and put that in. I'd advise against using it in same certain cookies because of the color it has or certain flavors. It mutes the nuttiness in a peanut butter cookie, for example. As in, it becomes fairly bland. I thought that was strange.
Cakes are usually made with white sugar because it cooks well. A brown sugar, be it from cane sugar, beet sugar, or the aforementioned alternatives, tends to give a wetter crumb because of the "impurities" present. Your cake will be dense if not discolored if it were a white or pound cake base. You would use a blend if you were making a brownie, chewy cookie, date cake, apple cake, banana cake, etc. You get the idea. For the brownie or chewy cookie, you won't get that shiny or matte flaky sheen on top for the brownie without white sugar, but you won't get the denseness without the brown sugar. You won't get crispy edges in a chewy cookie without white sugar, but you won't get that chewy if not fudge texture in the very middle without the brown sugar.
If you used butter for a brownie instead of the classic oil, you would have a cake like brownie via chemical reaction. It's why oil is the preferred choice unless you used browned butter which burns the milk solids and drops them, flavoring the clarified butter which you could use because at that stage, it's simply an oil with a high smoke point and won't react.
Molasses come in different forms. The most traditional is made from beet or cane sugar. You have different grades and even the harshest which is blackstrap. Then you have molasses made from fruits, particularly grape, which is the second most common. Molasses in general is considered an impurity because of what it is, being a byproduct, but also because of its mineral content. In other words, historically, molasses was given to children, the elderly and the ill because of how nutritive it could be. Especially blackstrap varieties. In many countries that rely on grape molasses, it's consumed by those earlier mentioned people, especially expecting mothers. Grape molasses to me has always tasted like those cheap hardboiled grape flavored sweets you had as a child, offset by an iron flavor and bitterness. Pomegranate molasses which can be found in North African cuisine is different. It's not typically used much and is better suited as a garnishing drizzle or accompaniment to a sauce. It's both very tart and sweet, without much bitterness. It's got an even 50/50 flavor in terms of tartness and sweetness. I'd compare it to reduced balsamic vinegar with sugar made as a traditional glaze. You could make both yourself, but it's a long arduous cooking process. I'd rather pay $15 for the bottle of reduced balsamic glaze imported from Italy. A small 500ml bottle lasts forever when stored properly and there's so few dishes or salads it's appropriate on that it lasts for years.
