What is this behavior?

I was wondering just what exactly my cockatiel is doing. When she's on my shoulder and I talk to her she puts her head down and makes a low tone noise, almost like a growling...yet she seems very happy, no the least bit angry. Also yesterday I got her out and she climbed up to my shoulder and I turned my head to her and she put her head down and her wings out, kinda like she was hugging me, but I really don't think that's what she did LOL. Just curious to see what some of these behaviors mean as I haven't had a cockatiel since I was little. The other day I had her out and she was on a perch I have set up for her and she flew in my direction, so when I got her she stayed with me until I put her in her cage. Yesterday the same thing happened. We visited my parents and she was on my mom, and she flew again in my direction (she's not very graceful lol) so I picked her up and she stayed there until we left, about an hour later. Does she recognize me, and try to come to me? or is it just my imagination?
She is 3 months old, and I'm not even sure it's a she. That's just what I've been told, so I have no idea...for now I'm calling it a "her".

It's happened to me before when I had a rabbit, they told me it was a girl, so I named her molly...later on down the road I noticed an "extra attachment" and so we named him Mo..short for molly since he knew his name.
I'm also looking for a name for my cockatiel, I've had her since Sunday and she's still nameless...so I'm open to any ideas anyone might have, I'd really appreciate it. She's the normal gray color variation.
And what are the chances of her talking? I had her whistling the first day I had her. And how long should I work on one tune, before I try to teach her a new one? Thanks for taking time out to read this post.
-Mandi

 

Oops, I messed up. This is the final post I intended to use. Sorry about that.
-Mandi

 

All young birds make slight noises when they are happy and content but the beahviour your discribeing is that of a 6month or older female wanting to breed.

Cockatiels are usually a one person bird and once they bond with one person they will know them just from the sound of there voice or smell of the aftershave or perfume.

Sounds to me like this little one has took to you with no problems and since she is only 3months old she is still a baby and looks to you as her mum and protector.

The wing display could be a sign to say to others around your stay away i will protect her and them putting out there wings makes them feel and look larger than they are to predators.

If she goes to sleep with her head under her wing while sat with you this shows she trusts you and feels safe enough to sleep.

Does sound like you have a little character there, You will notice too that as she gets older she will be able to detect when your feeling ill or down in the dumps and she will find a way to try and cheer you up even if it means her coming over and playing with your hair or ears.

Once she has mastered one tune you can then move on to another one but always still use her original tune during her training you will find like mine they learn very quick and can do a few tunes, Also if you start using words like hello baby things like that all the time when you cleaning out the cage or she is out with you she may also learn these aswell.

Mike

 

Mike, thanks for clearing up my questions. I love the little noises she makes they sound so sweet like she's trying to whisper to me. Sometimes she does this while nibbling on my face. She likes to give "kisses" as well. She normally has her crest down while grooming me, where I read that's when they are angry. I disagree, she seems very content while grooming me and has not once attempted to bite. The site I read this at is....

http://www.cockatielcottage.net/main.html

I found this a very informative site and interesting to read, especially being rather new to this kind of bird. I didn't agree with a couple of things, but the rest of it looked to be very logical and helpful.
This afternoon she was out on her perch and flew over to my husband, and actually landed on his shoulder. She sat there for a good 15 minutes until I put her away (was going to make lunch) and when I walked around the corner towards them she came to me.
The pup is extremely jealous of the bird. You can especially tell when you talk to the bird, the pup gets just as close as he can! So of course we spend extra time with him so he doesn't feel left out. He's still rather young, he'll grow out of his jealous stage sooner or later. Thanks again Mike.
-mandi