How do starches, butter and milk interact from a culinary chemistry / food technology standpoint?

I'm trying to find out how different starches behave and how they interact with other ingredients. Corn starch (Maizena), for example, will act as a thickener as soon as it reaches its gelatinization temperature. Wheat starch (wheat flour), on the other hand, only achieves the proper texture after having been mixed with butter or margarine and then with milk or cream, after which you need to reheat it to the gelatinization temperature of the mixture.

When making mashed potatoes, the boiled spuds themselves remain crumbly when mashed, in spite of the fact that the boiling, in spite of the fact that the boiling has gelatinized the potato starches, and only after mixing them with butter/margarine and milk/cream the consistency of the potatoes (i.e. the structure of the starches) changes to the desired creamy mash.

I'm also not entirely clear why, when making sauces or mash, one first adds butter and then milk, seeing as milk and cream both are a suspension of butter particles in water.

So.

Question 1: what is the difference between these various starches that makes them behave so differently?

Question 2: how do wheat and potato starch interact with butter/margarine and milk/cream (and why do these have to be added in that order) when making a sauce or mash, respectively?

All suggestions (and pointers into the right direction) are greatly appreciated!