Living things have bioelectric/electromagnetic fields. This is just a reality. Sharks, for example, can sense these fields given off by prey using special organs called the ampullae of lorenzini.
"Energy" is kind of a weird general term so I'm always careful when people talk about it if I'm not 100% sure what they are getting at. Opening oneself up to the energies of the universe reeks of letting down one's guard against spiritual powers. But there are electromagnetic forces tied to living things and emotions can affect them. Can they be intentionally manipulated? By controlling one's emotions and thoughts, probably. By other means, scientific/physical or mystical, probably.
The Bible isn't a tome of all knowledge so some of this stuff just isn't discussed there. There's biblical, aligned with what the Bible teaches, unbiblical, directly contrary to what the Bible teaches, and extrabiblical, simply not discussed by the Bible at all. This is where the discipline of "trying the spirits" - or evaluating sources of purported truth - becomes important.
To answer the OP I think pain is not an emotion but a sensation; however, sorrow is an emotion, and its relationship to pain is difficult. Sorrow can actually be so intense that it overwhelms all sensations of pain for a time.
Animals can certainly feel pain. I don't know if they can feel emotions like sorry. It seems like it sometimes, but as
@Lynx mentioned, you can usually write such cases off as self interest or instinct.
I see animals as biological machines. They have breath, and the Scriptures are clear they are to be treated humanely, but they are in all non-physical ways inferior to human beings.