Why did the Creme Brulee end up with lots of oil

Typically you should use yellow onions for cooking. They have a higher sulphur content and are more flavorful after cooking. Raw, a red onion will taste more pungent. However, once cooked it is more mild and sweet than a soup would require. Red, as well as other sweeter onions, have more sugar and water than their yellow counterparts. For more details on the profile, seriouseats has good primur.

If you wish to improve your results, you might slice more thinly and add some salt in advance of sweating (rather than before adding broth) to draw out the excess moisture, as the onion's moisture (more prevalent with red onions) will inhibit browning, ergo inhibiting caramelization and the maillard reaction that break the bigger sugars into little ones and lend flavor through browning. The explanation at norecipes also adds that deglazing with sherry can slow down the process if you are experiencing uneven browning. Another possible tactic would be adding a 1/4 teaspoon of baking soda per pound chopped onion; this will speed up browning.

Ultimately, unless the recipe calls for red onions, you are going to get better results with yellow onions in terms of raw, "sweet and tangy" onion-y flavor. You can use the tips above to try to overcome that, but a nice big bag of yellow onions are going to do you better in the long run, and if you put the same effort into the it will take less time, taste better and be less expensive.

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.