crack on (with something) - to work hard and to do something quickly (informal). Not seems to be a four-letter, but the meaning may depend on the situation and intonation. "We'd better crack on (with our task) before it gets dark." - sounds rather mild, because we say it to ourselves. "Crack on you two!" - Пошевеливайтесь вы там оба! - sound a bit rude if you are a boss speaking to subordinates, but normal if you are a mom of a pair of twins.

Hello, its an informal way of asking someone to do something more quickly, or to start doing something again after you have stopped for a little while. It means to get on and do something to get it finished.

yes

We do not use this term in tbe USA. It seems to be a British saying.

Very informal. means same thing as "move on." It's British English, it wouldn't be understood in American English the first time someone heard it.