Fire exposure

Are monsters with Fire resistance cannot be inflicted by Fire Exposure by Elementalist?

While playing i see there is no 'Red fire' indication under left corner of monster's life bar with this type of resistance.

Not that I'm aware. There might be some mobs that are immune but not simply because they have fire resistance. I think the little flame icon you are talking of shows when they go into negative resistance to that element. So if the have a lot of fire res, they have less, but still a positive value. I think in this case the icon will be on the right instead of the left, or possible neither if 0. You are still lowering it though. I might be misunderstanding the question if this is not what you are asking about.