So what really is up with her? What powers does she have, if she’s not Kryptonian?

Mae Kent, the second main Supergirl (1988-1996) is a humanoid being made of ‘protoplasm/protomatter’, a fictional substance created by an alternate universe Lex Luthor. She was then mentally and physically designed by him based on the alternate universe’s late Lana Lang. after his death, she regained her memories of her time in his lab.

She is able to shapeshift and turn invisible due to her ability to modify her own molecular structure. She is capable of mimicking a human perfectly, with internal organs included, as she passes as a healthy human to the eyes of a trained doctor. She struggles to increase her mass, however, and it causes her great pain.

She has telekinetic powers, and maintains a telekinetic field around herself that protects her from extreme temperatures and projectiles, as well as most attacks. She’s able to extend her shield to protect others around her as well. She is able to use ‘psychokinetic blasts’. presumably her telekinesis/psychokinesis is what gives her her enhanced strength and flight ability. She is vulnerable to fatigue.

She was psychically connected to Clark Kent / Superman in 1989. a 1993 promo card claims she still has this connection to him, but the link itself is never mentioned again within the comics. She is vulnerable to mind control and telepathic attack, as is shown here, and in panic in the sky with Brainiac, and in the New Titans arc with Raven.

In Action Comics #706 it’s shown that she can alter the molecular structure of other materials outside of her own body as well. This is never mentioned again, but perhaps is a combination of her unique biology and telekinesis powers.