Is there a ratio of how much water, fats, dry ingredients and flour to temperature and cooking time for cakes?
For ingredient ratios, the keyword is baker‘s percentage or baker‘s math.
Typically the flour is taken as the base value and all other ingredients are described as a percentage of the flour weight. Most home bakers come across the term when starting to venture into the theories of bread baking (King Arthur has a nice introduction here), but the same principles apply for other baked goods. A very famous example is the pound cake: originally using 1 pound each of flour, fat, sugar and egg. If you want to make a smaller or larger amount, you still use the same ratio.
Note that while in home settings we today typically count eggs and (at least in some countries) use volumetric measures instead of weight, in professional or larger-scale context ingredients- even eggs - are weighed. The importance of weight becomes obvious in recipes that are famously finicky like macarons, where some recipes recommend weight the egg whites and then calculating the remaining ingredients.
Older recipes for cakes, especially cake types which need rather precise ratios, are often based on the weight of the eggs. (Eggs come in “portions” and using “half of an egg” is impractical.) While today eggs are sold in weight ranges and a “size L egg” is pretty consistent, the eggs produced by a flock of chicken can vary a lot depending on the individual bird and the breed. So a cook or baker had to measure the amount of egg used for each batch of cake and adjust the other ingredients accordingly.
For references, you can either compare multiple recipes for a type of cake and calculate the ratios (or ranges thereof) or you check references for professional bakers or apprentices.
Temperature and time are a different matter. There are typical ranges for various baked goods and times will depend on the amount and thickness of batter, shape of the mold etc. A linear conversion like for the ingredients can’t be given. Just check existing recipes and work from there.