Parakeets do not become pregnant, they lay eggs. Females have a pink or tan color nostril band.
Parakeets have a beak and the thing above it which is called the cere.
a cere
Right above its beak.
Parakeets breath through their cere, The small but cute set of openings located above their beak.
That's normal. A parakeet's cere usually changes color after a year which is how you determine its gender. If I'm answering your question right, the "beak" you are refering to is the fleshy part above the beak. If the beak (yellow-ish-orange-ish keratin area) is changing color, you should take him/her to the vet.
I don't completely understand but if you mean the thing above the beak is turning pink it means it's a girl.
no, I have budgies/parakeets and have never seen that, and from what I've seen it's not possible.
Take them to the vet. Feel better!
Parakeets do not have teeth, they have a beak and a tongue.
If a parakeet's beak is blue, it's a boy. If it's red/pinkish, It's a girl!
a cere is the fleshy area above the beak surrounding the nostrils
If by face, you mean the cere (area above the beak, surrounding the nostrils), then no it just means that your female is not in breeding condition. I think parakeets more naturally breed in the spring, so if you wrote this anytime recently (ie winter), this is normal.