8. I (want) to figure out the meaning of this saying: "The pen is mightier than the sword." I (know) that "mightier" (mean) "more powerful," but what's a "sword"? What ("sword" mean)?
9. Right now Martha is in the science building. The chemistry experiment she (do) is dangerous, so she (be) very careful. She (want, not) to spill any of the acid. She (be, always) careful when she does a chemistry experiment.

8.
I want to figure out the meaning of this saying: “The pen is mightier than the sword.” I know that “mightier” means “more powerful,” but what’s a “sword”? What does “sword” mean?

Sword — это меч: оружие с длинным острым металлическим лезвием. Пословица «The pen is mightier than the sword» означает, что слова, идеи, книги, журналистика и убеждение могут быть сильнее насилия или оружия.

9.
Right now Martha is in the science building. The chemistry experiment she is doing is dangerous, so she is being very careful. She does not want to spill any of the acid. She is always careful when she does a chemistry experiment.

Здесь is doing и is being описывают действие и поведение Марты прямо сейчас. Does not want употребляется в Present Simple, потому что want обычно обозначает состояние, а не действие в процессе. Is always careful говорит о её постоянной привычке быть осторожной во время химических опытов.