Yes they have. In addition, they may have more senses than us. Even telepathy has been proved to exist, the only difference is that human people lost that ability (a part some rare exceptions), but animals probably can use it without problems.
In addition animals always lived in touch with natural environment, while human people lost this. Animals are more willing to be in tune to the environment.
I believe they do. They have a natural instinct that is a built-in radar to an earth event. I've noticed that whenever my cats get really nervous and won't settle down, a natural occurrence, like an earthquake, tsunami, or major volcano eruption in some part of the world, usually follows. It goes without saying that before a major thunderstorm or tornado locally, the birds get quiet and my pets get antsy.
They certainly do! Dogs in particular seem to have a sixth sense about people (good and bad) and about impending storms. They also know when to be gentle, with a baby for example. Birds stop singing when a storm is on the way and then sing their little hearts out when the sun shines through once more. We have too much distracting us to be so attentive to the world around us, which is a shame. Maybe if we woke up and smelt the roses the world would be a better place (before there are no more roses to smell). Great question! Ann