1 Yes, thanks for spotting it.
2 It's fine as it is: AskOxford: coalface
1. Should it be "an office"?At the coalface - Idiom Definition - UsingEnglish.com
If you work at the coalface, you deal with the real problems and issues, rather than sitting in a office discussing things in a detached way.
2. Is "coalface" one word or two words ("coal face")?
There is a related term, first used a reference to 'coalface', emphasizing the more onerous aspects of teaching: example - 'Lots of directives come from various government departments about what should be happening in schools, but teachers at the chalk face know what is really happening.'
This is a reference to a kind of teaching that I knew when I was in short trousers (or as they say in America, 'knee pants'), though as a teacher I have never used chalk. Like many metaphors, it is stuck in a time-warp; a modern phone is still 'off the hook', teachers are 'at the chalk face', young children call diesel locomotives 'choo-choos' even though they've only ever seen a steam locomotive in a museum or in a picture book...