Generally it would mean that after they have finished putting on their makeup (their face on) they will not cry. I hope this helps.

This refers to girls putting on their makeup. Sometimes, makeup can be seen as "battle armor" because it presents you as suitable and ready to go out and tackle the day. This lyric can be interpreted as a metaphor for putting on armor, or a facade, in order to go out and be ready despite what they might be feeling inside.

It means to make a face at someone. Moving your eyes, mouth, nose to make someone laugh or show emotion. For example, you may smile because you are happy. If you would like help with idioms, I am a community tutor here and would be happy to help you understand idioms.

Thank you

put make up on their face