The word "treat" has multiple valid meanings depending on context:
As a noun, it means a reward, delight, or special pleasure.
As a verb, it means to give medical care, to behave toward someone in a particular way, or to deal with something carefully.
Sentence I: Correct - "ice cream as a treat" is an appropriate use of "treat" as a noun meaning a reward or special delight.
Sentence II: Correct - "treat the infection" is an accurate use of "treat" as a verb meaning to provide medical care.
Sentence III: Correct - "treat the old painting with caution" is valid, as "treat" also means to handle or deal with something in a certain way.
Hence, the correct answer is option (e): All I, II, and III.