Unfortunately I can't write a story for you, but you can make some story up where your father saves you from running into oncoming traffic on a road, or where he saves you from choking on some food. I'm assuming anything will work
I'm pretty sure it's "the baby cried" because an independent clause can stand alone and that can stand alone.
Yes it is a full sentence
Answer:
The cafe Buzzed with activity, it was cozy and buzzed noisily.