Yes, animals do have emotions and also distinct personalities. They also have different psychological traits.

Emotions: Pretty easy to verify, just think of any animal (wild or domestic) and how they react to amicable vs. hostile behaviour. A dog you've made happy by giving him a treat will wag his tail, an angry bee will chase you down the entire street and probably further if you threaten her hive.

Personalities: I don't know if you've ever had pets, if not perhaps you can think of someone you know who does. If for example you have more than one cat or more than one dog, you'll notice pretty soon that each likes different things (foods, toys, favourite places, etc.) and behaves differently around people, other animals and so on.

Psychology: It is possible to traumatize animals. Animals rescued from labs for example act and behave completely differently from other animals of the same species and usually never recover. Animals whose owners used to beat them or that have experienced a traumatic event early in their life exhibit abnormal behaviour when "triggered".

As for a moral code... I think that's a little more complex. It depends on your definition of a moral code and on many other things. In all honesty I couldn't answer your question with a "yes" or a "no".
One thing I'm absolutely sure of, though. What you won't find in an animal is unfounded hatred, prejudice or malice. If you think about it those are things we find only in humans. Wars, genocides, torture, slavery, abuse, systematic slaughter of dozens of species, destroying one's own habitat... all these exist nowhere in nature but in the human species. In this sense, if I had to pick who's more moral - animals or humans - I'd say animals in a heartbeat.