Here's what I have so far...
Copycat is a human merged with the body of an extradimensional being that has simulated the appearance of her deceased best friend. Her alien body was a weapon, designed to mimic beings it encounters, but she has either lost or is unable to access the shapeshifting abilities of her alien body. The only power she retains is her ability to copy powers from others. She can mimic the power of a single individual upon touching them. The power lasts until she replaces it with another power, or decides she no longer wants to keep the power. Along with the power she copies, she generally gets any associated weaknesses, and sometimes picks up personality traits or strange interests and hobbies from her subjects.
As the body was designed to fight, she retains its skills as a fighter, though they are more combat reflexes than anything of which she is consciously aware. Her memory is phenomenal, and she sometimes retains skills and knowledge from those she mimics. Part of the alien design was to assimilate information about its surroundings, and that seems to have bled over into her personality; she is highly interested and knowledgeable in current events and pop culture.
Nyssa was a plain girl of average intelligence, but a gifted telepath. Growing up, she couldn't help but read the minds of those around her, and the idle thoughts and petty judgments of her friends caused her to develop a self-confidence issue. She could hear the guys all thinking about how gorgeous Jenny was, imagining her naked, or worse still, doing disgusting things with them naked. She could hear Jenny's thoughts abut Kim's cute outfits, or Julie's lovely shoes, but never anything so flattering when she saw Nyssa. She came to believe that she was nothing special, and that boys would never be interested in her, and to wish over and over that she were Jenny instead of boring, plain Nyssa.
Her telepathy made it hard to make and keep friends, but she did find a few who didn't seem to judge her, oddly enough Jenny was among them; it seemed the most beautiful girl in school was also fairly easy to block out. Nyssa found that she could spend time with Jenny without reading her thoughts, something she found difficult with others. They became the best of friends, and even deiced to go to the same college. Tragedy struck on Jenny's twenty-first birthday; the car she was riding in was struck by a drunk driver and she was killed instantly. Nyssa was devastated, but after months of grieving, finally found the strength to move on with her life.
She never revealed her powers to her friends, but in her junior year at college, she was discovered by another telepath, Rose McEwan, the retired former superhero Psyche. Rose was a professor at the college, and also contracted her powers out to a corporation (possibly Dark Water Industries?). Sensing her potential, she took young Nyssa under her wing (and collected a large finders fee from the company.)
Nyssa spent several years letting the company test and catalog her abilities, and eventually was tapped for a new project. The company had discovered extradimensional travel, and had begun opening portals to multiple dimensions. After the first incident, the company began to use telepaths to reach into the new dimensions before sending explorers and risking the lives of their people.
Nyssa was hooked to a cybernetically controlled machine, searching for sentience telepathically in the other dimension they had accessed during their experiments. Day after day, she found nothing. But then one day there was something there, a mind, a presence. The being she discovered was curious, inquisitive, and unknown to her, had evolved to mimic, slay, and replace anything it contacted.
The telepathic link allowed it access to her mind as well, and it took the form it saw there, her ideal form, the way she always wished she looked: the image of her high school friend Jenny. Nyssa could sense the alien mind, knew it wasn't human, but it was Jenny, and she needed help. She couldn't just leave her there, in that alien dimension. Maybe Jenny had fought her way back from some sort of afterlife and was trying to tell her something. She had to know, she had to do something.
That something was to let it in; a choice she couldn't make on her own. She reached out telepathically, and for the first time since she was a small child tried to control another mind. Panic and hope at seeing her friend again made her strong, and she forced the technician to open the portal wider, wider, let Jenny through! Then everything happened at once.
The Jenny create lunged into our world, caught in the containment field. Nyssa tried to extract herself from the machine to help Jenny, and the rest of the technical crew caught on to what was happening and tried to shut everything down with the kill switch. It was too late. Nyssa lashed out, the psychic attack holding the techs just long enough for her to reach out at touch Jenny, and then everything exploded.
Nyssa awoke in a hospital bed. Her body felt wrong, she couldn't concentrate, couldn't think, everything was foggy, there were no thoughts but her own. She couldn't hear them anymore, she was alone in her mind. When she headed to the bathroom, she caught her reflection in the mirror, and she gasped. She was no longer Nyssa. She had been replaced by a beautiful woman with a perfect body, the mirror image of her best friend Jenny, the most beautiful woman she had ever known.
Slowly, step by step, her mind recreated the events of the incident. The portal was not designed to transport anything, just access the other dimension, but somehow Jenny had come through, or the thing that looked like Jenny. When they touched, they had become one. They had merged. Her mind had been stronger, and remained. The other worldly Jenny must have been the stronger of the two bodies, and remained.
The company had decided she was now an asset, and wanted to dissect her new body, discover its secrets, but her mentor Rose used her telepathy to help her escape. Tactical teams were dispatched to stop them, and when their hopes of escape seemed impossible, Rose sacrificed herself so Nyssa could escape.
Alone, with no money, no family that would recognize her, no identity other than that of a dead girl, Nyssa lived on the streets for several days. On her third and hungriest day, she was attacked and nearly raped, saved at the last minute by (insert member of the Cadre here). When (hero) helped her up, her powers kicked in, and she copied (hero)'s powers. Seeing her abilities, she was invited to come back to Overwatch for observation, and eventually given a place on the team.