When my child turns 18 years old. Will either him or me still get Medicaid if financially qualify?

In the states that expanded Medicaid you qualify as long as your income is under 138% of the Federal Poverty Level. All other states do not give welfare health coverage to able bodied adults, so you'll need to qualify through low income and disability.

He has to apply himself and include all household income on the application and answer other questions. They should get a job and get insurance and forget about government welfare.

Maybe. It depends on where you live. In some states, yes. In some states, no.

We don't have a clue without actual info.
Try actually asking local educated adults in ur area.