Are emotions merely forms of communication? What are their evolutionary purpose? What purpose do feelings of guilt, remorse, shame, bitterness, pride, and love serve in the evolutionary process?
I know that emotions aren't exclusive to humans, but I don't understand how they have 'developed' over time.
I think you are asking too big of a question and you need to break it down. How did emotions develop? What is the evolutionary process? Well that depends on what emotion you are asking about.
I hope you understand that when talking about the modern Theory of Evolution that it is all about the genes. It is about a survival advantage to the genes, not necessarily to the organism.
Fear and sexual attraction for instance should be immediately obvious. You need to survive, to avoid danger and find a mate in order to pass on your genes.
I can hear what you might be saying to this, “well that is fine for base emotions like sexual attraction, but what about higher emotions like love”?
Well what kind of love? The love a parent has for their children is clearly also an advantage in protecting their own genes. The love one has for their mate is also an advantage in forming a bond for raising their children (protecting their genes) together. Love for your neighbours or friends creates a safe community, which again is advantageous for raising your (genes) children.
How about guilt, remorse, shame? We humans live in a society; we evolved to live in a society. To be able to survive in a society we need to follow certain codes of behaviour. Guilt provides a negative reinforcement for following those rules. And pride provides a positive reinforcement for the kind of achievement that it would be advantageous to repeat.
This is just a short list of a few emotions. Others may be more complicated. Some may be as Wandered Off suggests a byproduct of another process. There is clearly no advantage for a moth to fly into a flame, but it happens as a result of another very useful process of navigation by the moon. Some emotions may have similar causes.
Hope that helps a little.