Different techniques in making creme brulee

In this case, the mixing order won't make that much of a difference. You need the sugar dissolved and the yolks broken up.
However, adding the sugar to the yolks will have two results:
- it will allow you to more easily break up the yolks but if you mix too much it could actually aerate them- not a big risk but not good thing for creme brulee.
- more importantly the sugar will give you a little bit of buffer to keep the yolks from curdling when you mix in the hot cream.

As for using just yolks vs yolks and whites.

Yolks have a lot of protein but they are very high in fat. Whites are just blobs of protein, of course. Using only yolks creates custards that are very rich and creamy but also high in fat (which is where "rich and creamy" comes from). Using the whites gives some of the needed binding power while reducing the fat a little.
Additionally- whole eggs are easier to use because the eggs don't have to be separated and you have fewer extra whites to use elsewhere.