Answer:
1. It is raining outside, we are prevented from going out.
2. Either he or I am not feeling well.
Step-by-step explanation:
1. When we complete the action expressed by the verb "prevent" with another verb, we should use the preposition "from" followed by the next verb with -ing. Other examples are: My advice prevented him from doing something silly. / I hope the increase in sales will prevent the company from going bankrupt.
2. In this case, the subject contains "either... or" and the pronouns "he" and "I". The verb will, therefore, agree with the pronoun that is closer to it. Since it is "I", we should use "am" instead of "is".