Language explosion

It seems like K's going through a bit of a language explosion over the last 1-2 weeks. I was getting a little worried that she wasn't picking up new things to say, but I think she's proving me wrong.
For ages now, she's been saying "uh-oh", "mama" and "papa". Then she started saying "teddy", "woof woof" (for any dog), and more recently "nein" (no) to pretty much everything. Sometimes when she says it, she doesn't really mean it. I'll offer her something to eat, and she'll shake her head, say "nein", pull her head away, and then turn back and open her mouth up to chow down.
She's able to point to more body parts now when asked: Nase (nose), Ohren (ears), Augen (eyes), Mund (mouth), Kopf (head), and Bauchnabel (belly button). Sometimes she doesn't get ears right though. It's so cute when she squishes her little nose with her finger. She tries to say "hei" (heiss = hot) when we say it, and then blows like she's going to cool whatever it is off.
She's been saying more animal sounds over the last 2-3 weeks too. She'll say "woof woof" for dog, "ooo" for cow, "ooaar" for lion, "aaa" for sheep. She grunts for the noise that a pig makes.
Over the last few days, she's started saying a few more things. "Baer" (bear), "baby", something that's "thank you", "baa" (ball). And she'll say "up" when she wants to be picked up or helped up onto something. It sometimes takes a little prompting to get her to stop screeching with her arms in the air and say up, but she'll usually do it. I think she's said "mo" (more) as well. And "shu" (shoes).
Our nanny says that she can also count to three when prompted, but she refused to demonstrate it for DH or me today.
I think things are going to get a lot more fun from here on out as she's able to communicate more and more. It's exciting!
She's still showing preferences big-time, but right now it seems to be Mama in favour. We'll see how long that lasts. She did get very made at me tonight when I told her no biting, after she chomped on my elbow and then my knee. Big tears and sobs from being sternly spoken to. She needed hugs from both of us after that.
She's great at helping to get pants on or off, or her shoes. She really hates getting her top changed these days though, and I'm not quite sure why. Maybe she got her head stuck at one point and got traumatized? If I take off a dirty diaper and go to dump it in the bathroom, she can now roll out of her changer. But if I come back and lay out a clean diaper, she'll crawl back into the changer and try to put her bum on the diaper.
K's also great at helping to clean up sometimes. When I let the water out off the tub after her bath, she automatically starts picking up her toys to put in the Bo.on frog holder we have for the bath stuff. She'll often put books away (on request) before getting out a new one. And she's very good at fetching things for us as well. I guess her comprehension is also improving lots these days, both in English and German.
K seems very good with her motor skills these days. She's good at getting a key into a lock, can pick the tiniest speck of dirt up off the floor, and is great at taking my cell phone out of its holder and then putting it back in. She dances (stomps her little feet, wiggles, and spins around) when music's playing, and can ride a sit-on trike without bumping into too much. She's cautious around stairs for the most part, and will stop and reach up for a steadying hand to hold to go up or down. She's pretty fearless at the park, and can climb onto most rocking things (like the big green frog) by herself now, as well as up onto the teeter-totter. She makes me a little nervous when she heads for the edge of the play structure where a bigger kid can climb down on a metal ladder or slide down a pole. I _think_ she realizes it's a big drop and that you'll catch her, but sometimes wonder if she'd throw herself off the edge if you weren't there. She's really good at throwing balls around.