Tomato plants are born with peach fuzz
They have the fine white hairs as a seedling and they have them on their flower stems. So yep, that's normal. The flowers are probably falling off right now because it's too hot for the blossoms to set (become pollinated).
Pruning the lower leaves is a controversial technique. Less foliage = less energy from photosynthesis. But generally, in humid areas, it's considered better to provide more air circulation. On the other hand, more leaves on the bottom means less sun pouring onto the plant and cooler roots. But diseased foliage should be removed.