Bądźmy mili - Let's be nice
Bądźmy życzliwi - Let's be kind
Bądźmy uprzejmi/grzeczni - Let's be polite
"Polite" is correct btw.
It usually translates to "uprzejmy", but yeah, you're right. Added.
Yup, well done!
What is the dictionary form of badzmy?
The basic one... well, "być". That's just a form of "to be".
https://en.wiktionary.org/wiki/by%C4%87#Conjugation - imperative, 1st person plural.