I am not sure whether the three sentence make sense in term of grammar and semantics.
Can you give me a hand with checking them
Thank you for your help.

1. What residents can improve their community is that they should apply their knowledge to inculcate others.

2. It is after attending a course in English that adults will attain more opportunities to get promotion.

3.If they are not good at English, they won’t discuss their project to their partners; not to mention make a presentation to brief the details about the proposal.
1. Residents can improve their community by using their knowledge to inculcate others.

2. After attending a course in English, adults will gain more opportunities for promotion.
3. If they are not good at English, they won’t discuss projects with their partners or make presentations on the details of proposals.

I believe I would have you consider a different word than 'inculcate'. Here is Merriam-Webster's definition:

Etymology: Latin inculcatus, past participle of inculcare, literally, to tread on, from in- + calcare to trample, from calc-, calx heel
: to teach and impress by frequent repetitions or admonitions

'Inculcate' has a degree of forcefulness to it that may be a bit strong for a concept of how residents should interact to improve their community.