1.Be sure to check it.怎么分析这个句子的成分，to check it是作be sure的结果状语吗？还是be sure to充当谓语，check it作其宾语？

——to check it作目的状语。

2.I devoted all my life to studying it.  to studying it作宾语补足语还是状语？或者studying it作复合谓语devoted all my life to的宾语？

—— to studying it是介词短语作状语。

3.同理，这个句子呢: Plan ahead for some activities.

——祈使句。plan是谓语；ahead是副词作方式状语；for some activities介词短语作目的状语。