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It depends on the animal specie. As more complex is the brain, more complex are the emotions. Who knows, some animals may have self awareness. Let me should the different levels of emotions in animals (this is, of course, just a theory based on the intelegence of animals, but it is very plausible):

1.not very inteligent; the only emotions are the very basic ones, like fear or anger. Animals in this level include most invertebrates, fish, amphibians, most reptiles.

2.a bit more intelegent; parental care is present, but nothing more aside from that. Examples include crocodiles, cephalopods (octupuses and squids), monotremates (egg-laying mammals like platypus) most birds and some prehistoric reptiles like dinosaurs (which are known to had parental care).

3.medium level; love and other more developed emotions are present, but they aren't as deep as ours. Most mammals, parrots and passerine are in this category.

4.higher level; self awareness is present, as well as all deep emotions. Elephaunts, cetaceans, some roedents, primates (including us) and perhaps canines and crows are in the higher level.

I do believe animals have feelings, indeed. I also believe that animals have all, if not more, than the feelings we humans have.
Although, we humans are more emotionally connected than the animals, thus making our emotions stronger.
But animals have weaker emotions, but better ways of showing it, than us humans, which I admire them for.

In short; yes, I think animals can feel all the human emotions, if not more than we can feel ourselves.

yes, If you know your pet well you can here it when they meow or bark and so on.