Hi! Both of these phrases are correct but actually have quite different meanings. To ask 'Does he have any fears?' would be to ask if he has any phobias. For example, a fear of heights or spiders. This might or might not be related to the situation at the time. 'Does he have any fear?' is quite different surprisingly. You might ask this question in a situation where the person is doing something dangerous or that is potentially scary and but they don't look scared. Maybe an example of this would be firefighters who run into a burning building to save people. Most people would be very scared, but often emergency services personnel don't show their fear (it doesn't mean they don't feel scared though!). So, you might ask this question in surprise because you thought the person should be scared.