Hey Anselm I am Mirage, wonderful greeter, ST of Alvadas and known as the hand of destruction to some. I am here to give you a hand with your questions
1) Yes Kelvics can understand their masters in any form (if they know the language at least), but they do not always think as you and I would. They may associate certain words with certain objects or experiences. For instance, if you rub a dog Kelvic's belly while saying "Good boy" over and over again, the Kelvic may come to associate "good boy" with getting his belly rubbed. Does that make sense? Basically, Kelvics think very simply, especially when unbonded, so more often than not they more associate words than completely understand their meanings.
2) Now I am pretty sure I understand your meaning, and I am afraid I must answer with a flat No. Kelvics Can Not Talk in animal form. Now, they CAN communicate. For instance, if your dog likes something it will wag its tail and look up at you with that dopey, happy expression they get. If they are scared they do that little whimper and tuck their tail between their legs. All in all, in animal form communication comes in body language, in how they move and certain sounds they make may lead someone who knows the Kelvic well to kind of guess at their meanings. Bonded Kelvics can potentially con vie their meanings in a more easily understood way (LIke a horse tapping its hoof to count for instance, or a dog nudging his master to move him from danger, ect...), but this is only after they have spent some time with their master and have learned to "think" basically. After all they are animals, and Instincts rule their actions. After so much time with humans though it is possible that they will obtain a bit of humanity themselves.
3) Your last question really has to do with the history of the Kelvic itself. If it is a wolf who grew up in a pack, then yes he would be able to communicate with other wolves. Possibly some other canniness that communicated in a similar fashion. However, if said wolf somehow grew up in a lavish environment and was pampered by strange humans who liked to keep him as a pet he would not necessarily be able to speak/understand the language of his kind. Now this is not always the case, as it may be that he sneaks off and runs in the wild and picks things up after a while, but generally someone cannot know a language unless they have been exposed to it.
Does this help?