1. I know (that) Tom likes Chinese fried rice.【解析】从句是陈述句，宾语从句连接词用that；主句是一般现在时态，根据语境，从句用一般现在时态。
2. The teacher said (that) the earth moves around the sun.【解析】从句是陈述句，宾语从句连接词用that；主句虽是一般过去时态，从句意思是表示客观真理，仍用一般现在时。
3. I don’t know if / whether they are fond of music.【解析】从句是be开头的一般疑问句，宾语从句连接词用if / whether；把are移到主语they后，保持主谓语序；时态与主句时态呼应，保持不变。
4. He doesn’t tell me if / whether she likes English.【解析】从句是does开头的一般疑问句，宾语从句连接词用if / whether；把助动词does去掉，保持主谓语序；主句是一般现在时态，在动词like后加-s。
5. Can you tell me if / whether he finished the work just now?【解析】从句是did开头的一般疑问句，宾语从句连接词用if / whether；把助动词did去掉，保持主谓语序；从句中just now是过去时态标志，动词finish后要加-ed。
6. He asked me if / whether we would leave for Fuzhou tomorrow.【解析】从句是will开头的一般疑问句，宾语从句连接词用if / whether；把助动词will移到主语we后，保持主谓语序；主句时态是过去时态，把移后的动词will变为would。
7. She wanted to know what they were talking about.【解析】从句是what开头的特殊疑问句，宾语从句用疑问词what作连接词；助动词are移到主语they后保持主谓语序；主句时态是过去时态，把移后的动词are变为were。
8. I asked Zhang Mei how she went to school every day.【解析】从句是how开头的特殊疑问句，宾语从句用疑问词how作连接词；does去掉，保持主谓语序；主句时态是过去时态，从句中动词go变went。