Are 中国 and 中华 synonyms?
In Modern Chinese, 国 means a sovereign state, e.g. 中国, 英国, 美国, 德国, etc. In ancient times, 国 could also mean a non-sovereign state, e.g. 楚国, 齐国, 赵国, etc. Anyway, 国 emphasizes the government's control of a specific land.

As a result, 中国 can only refer to the sovereign state that is named China, while 中华 is more likely to refer to the ethnicity or nation that is named China.