In Skyrim, what does a full armor set entail

She won't use Elven stuff because it's weaker than her heavy type Steel armor, I guess because she's skilled in Heavy Armor and not in Light Armor. I've given her Dwarven stuff and she equipped it on the spot myself.

As for why she did equip the elven helm, well she doesn't have a helm at all in her default gear so any helm is better than what she has no matter the stats.

The easiest way is Smithing and Enchanting. Barring that, simply level up. As you do so, Merchants inventories, quest rewards, and items found in the wild will improve.

Alternately, you could pursue some of Skyrims fabulous and exotic Artifacts, which are non-levelled magical items of exceptional power. Several of the Daedric ones are particularly good.

In the case of Armor, one important thing to note is that there is technically a 'cap' of 567 Armor - 80% physical damage reduction. A fully Smithing upgraded set of Hide armor yields somewhere in the neighborhood of 700 Armor with all the appropriate perks, so realistically, you can wear whatever looks good or has enchantments that you're fond of once you have the appropriate perks and upgrade it at a workbench.