Bread flour has more gluten than cake flour. Gluten is the protein in flour that produces elastic, stretchy dough and chewy breads.
Cake flour has less gluten in it. Gluten is in wheat flour. It is what gives bread it's texture and structure. cake flour is a soft summer wheat as is pastry flour regular flour and bread flours are a winter wheat a lot more gluten Cake flour is softer and more refined than all purpose flour, if the recipe calls for cake flour then do not substitute for if you do the results will not be the same.
There are flourless cakes. They are denser than regular cake but can be eaten by those that have gluten problems. They use more egg than regular cake.
Cake flour has less gluten than bread flour, but it does contain a significant amount of gluten. While these estimates should not be taken as authoritative, cake flour contains roughly 6 - 8% protein (gluten) compared to about 11% in all-purpose flour, and about 14% in bread flour.
Yes, cake mixes are made with wheat flour, and all wheat flour contains gluten. Cake mixes contain less gluten than bread mixes or all-purpose flour, but still enough to cause problems for those who are gluten-sensitive. Betty Crocker has a few gluten-free cake mixes on the market, but in general, you'll need to use scratch recipes that use rice flour, or almond meal. If you do a search for "flourless cake recipes," you'll find a few good ones, though they'll be much more dense than what you get with a boxed mix.
Cake flour has less protein than all-purpose flour not less gluten. If you are baking for someone who needs gluten free, Cake flour will not help. You will need a combination of tapioca flour, potato starch, xanthum gum, rice flour, and possibly others. There is also a product called Bob's Red Mill all-purpose Gluten free flour that works pretty well as a replacement to regular flour.
All purpose flour cannot be converted into cake flour. They are two different types of flour that are milled (ground) differently from different types of wheat. Cake flour is lighter, finer and has less gluten than all-purpose flour.
I would think you mean Madeira cake rather than Madeira wine. If so, Madeira cake is not gluten free unless it is made with a gluten free substitute for wheat flour.
Plain flour, which I also use to replace cake flour (although cake flour would be lower in gluten than our plain flour, but we don't have an exact equivalent.)
"Baking flour" is not a familiar designation. "Bread flour" has more gluten than "all-purpose" flour, and is the best choice for bread, but "all-purpose" flour is perfectly acceptable and should produce a successful bread dough. "Cake flour" has less gluten, and is formulated for cakes and other products where a tender crumb is desired. Breads made with cake flour might not rise properly.
When "worked up" by mixing or kneading, gluten makes dough elastic and the finished product chewy. This is desirable in bread but undesirable in cake which should have a "tender crumb" without being chewy or tough like bread. This is why bread flour has higher gluten content than cake flour.
Bread flour has a higher gluten content than all-purpose (or cake) flour. Gluten is what creates structure in wheat flour and while all wheat flours contain gluten, the higher percentage of gluten in bread flour will create a more rigid structure, lending to a chewier, tougher crumb and texture.
Bread flour, sometimes called "Strong flour" has a higher gluten content than regular cake flour. Out of all bread flours, "Canadian" bread flour usually has the highest gluten content. I think that pasta flour (sometimes called "00 flour") may have a slightly higher gluten content than some bread flours, but using pasta flour doesn't result in a better quality of bread.