If I shout at her, the shout goes right through.
If I attack her, she doesn't take damage or even get hit.
If I ask another follower to attack her, same thing.

Attempting to pickpocket her only results in a conversation starting, and not actually pickpocketing.

What's up with this?

You sick [censored]. How could you possibly want to harm Serana.

I want to do this (from the UESP forums):
"Just upgrade regular Vampire Armor to Legendary status have her wear it, dismiss her and as she walks away picpocket her Royal Vampire armor. Then ask her to follow you again, trade items with her, remove the Legendary Vampire armor you gave her. After that you can give her any equipment and she will wear it. Just dont remove her boots or her starting equipment will appear back on her."

I don't actually want to attack her. I only realized that it couldn't be done when Aura Whisper WASN'T detecting her, and I couldn't pickpocket her (the option was there it just wouldn't work).

Not sure what they are talking about, but:

I put her in ancient falmer armor (3 piece set, enchanted to legendary), Auriels shield, dragonbone sword one hand,
and a necklace ring (all double enchanted for the stuff she does too, like mostly destruction lower magika cost, one conjuration
lower magical cost, some one hand where nothing else would go.)

She happily wears it all, looking cool in the ancient falmer. I never had to do any of that stuff they said. I did notice
that I can't "pickpocket" her for gear anyway.

So she wears stuff anyway, its all equipped when I look to trade things with her (as well as being visibly equipped.)
Even the necklace and ring I made for her gets equipped by her.

She even walks around with the dragonbone sword and auriel's shield equipped (that shield goes well with the
ancient falmer armor too ), though she switches to her red svck life/frost/whatever destruction when there
is a fight.

Perhaps the quote you have is talking about a difficulty with getting her to wear vampire robes or such, because
to her the original royal vampire robe is better? She'll certainly happily wear armor though, or at least
the ancient falmer light stuff (first set I tried on her, actually, lol.)

Yes, that's correct. I want her to wear clothing or items with 0 armor rating.

That said, I find it frustrating that everytime I give her a piece of armor and no helmet, she wears that hood of hers 24/7, even indoors. Is there a way to remedy this? I don't like having my followers wear helmets. Everyonew who follows me wears a circlet happily, in place of their own helmet. Serana is the exception.

Serana wears a circlet i gave her, but randomly she will also use her hood or have no headwear at all. But cant get her to wear atherial crown at all.

I'm fine with having no headwear--that's what I'm trying to achieve by giving her the circlet. However, she seems to wear her hood 24/7.