Is it possible for a 3 month old cockatiel to molt?

Okay, lots of questions

So it is pretty much impossible for a full molt to happen this early. She may be replacing some damaged feathers - but more likely she is transitioning into another stage of juvenile feathers. When a cockatiel gets its first set of feathers in the nest, the flights and tail feathers are short to accommodate the nest and are very ill suited to flight. They usually go through a partial molt that gives them new primary flight feathers and sometimes new crest feathers and patches of darker body colors. Think of this as the awkward adolescence. She still won't have a complete molt and transition into adult feathers until six months. I didn't experience this with Pirate, he was already in the process of getting these transition feathers when he came home with me. She will still be awkward and baby cute for awhile yet, don't worry

Second, if she has painful pins, then make sure to encourage her to enjoy misting or coming into the shower with you. Even if she doesn't want to splash about in the shower, the steam and increased humidity will give her aching feathers a reprieve. As the pins grow longer, don't avoid touching them. Be very tender and gentle, but keep trying to rub under, over and around them without pulling or pressing too hard. The pins shell won't break open easily on is own, and she can't open the ones on her head by herself. Plus, they itch like the dickens, and gently rubbing them and the skin around them will comfort Pepper through the cranky stage. That is why mutual preening is so important to birds. It will strengthen your bond. Most importantly, don't push them down into the skin. That's what really hurts! Brand new pins might be too sore for this, take your queue from her. But once they come out of the skin more and more, you will need to try to keep touching them.

Don't ever pull out a feather that is not a broken blood feather. Depending on the age of that particular feather, she could bleed profusely, and no matter what the age of the feather, it will hurt and she will be angry with you. If the feather is bent over and part of it is sticking out at a funny angle, I recommend clipping it at the bend. That way it won't get stuck anywhere it shouldn't, and it won't hurt Pepper at all.

Probably in a limited way, enough to control her descent and train her flight muscles. Pirate didn't really take to flying well until he was starting to get some adult feathers, but then, he was never given the opportunity to learn until I got him around four to five months old.

Thanks Pammy! I sometimes feel like she has a mischief expression, or she's genuinely smiling other times. My spray bottle broke before I was able to give Pepper a good spray down (that's what I get for buying one from a dollar store haha!) Later on tonight I'll shut the bathroom and let it fill with steam so Pepper can enjoy some relief from those pins poking out. Thank goodness she's not being crabby towards ME. Bubbles and Whisper, on the other hand are getting it. 

Sarah, did you do anything special to sort of teach Pirate to fly since he hadn't learned when you got him? 

On an off track update, Bubbles now lets me pick him up without biting me. He comes out of the cage when Pepper is out and they both jump off the cage top at the same time. Whisper is Whisper, no improvement yet haha. 

Oh dear haha! I'll definitely have to start getting Pepper used to flying. We do the "drop and rise" on the finger and she opens her wings to "glide" but other than her dive bombs off the cage, I haven't started her flying school yet ^-^ I HAVE noticed she can glide a little farther from her cage now. Not sure if that's from feather growth or her practicing. 

New cockatiel worried owner here: Lucy has these thin, longer thread-like "hairs" sticking out of her neck/head, I don't think they're "pins", they aren't hard or stuff they're just like little hairs, does this mean she's molting? Do I need to pay any special attention them? Pulling them out or scratching or anything? 
Shes still much younger than Pepper so I'm not sure what they are

I have the cutest video of her to post... I especially think you will like it (you'll see why!)

Hi Suzie,
I am glad you have found answers. I do not own any more birds at the moment but I will help best I can!

Hannah