Hospitals are useful for us because in hospitals sick people are treated.
If the capitalization for the first sentence wasn't on purpose, it's A. If not, C.
The sentence that contains a boldface infinitive is D. Lisa wants TO GO.
It is easy to spot an infinitive - it is usually a combination of the word TO plus a verb.
A and C are incorrect because those are not infinitives, but rather prepositional phrases. B is incorrect because it is an infinitival phrase, rather than a single infinitive.
This one: "Lee noticed a problem and alerts a teacher".
The second verb should not have been changed to present tense.
You should change the verb alert to past tense: "Lee noticed a problem and alerted a teacher".