She did inherit a mix of her parents' quirks. Her father has the ability to gather energy and form it into attacks, such as blast attacks, or even healing— so long as he focused his energy on what he wanted it to do— and her mother has a monkey-like tail. Therefore, Fasha has a monkey's tail along with the ability to create energy attacks. It's powerful and can be utilized in many ways, making it seem like she has multiple quirks, when really, it's only two.

Monkey Tail

She can use her monkey tail in the same ways that monkeys can. She can grasp things with it, which she often does when she runs out of hands. She's even taught herself to write with her tail, and is also capable of writing with her feet. Because she can use her tail in such ways, she uses it in fights as well, wrapping it around a person's neck, wrist, or ankle to jerk them forward, and she can use it to slap people as well— it does really hurt, too.

Other Ape Attributes

Because of her mother's ape/monkey quirk, she has more than just the tail and the feet, but also has increased strength, speed, agility, durability, and the like. She's much stronger than she looks, and because she can combine it with her father's energy quirk, she can "level up".

Power/Energy

     She can use them in small attacks or large attacks, and the only way to explain it would be by using Dragon Ball Z terms, so she's been told. She hates being called a Saiyan (at least at first, but she later learns to accept it as her hero name suggests), but she is almost just like one.

     Because of the energy that flows through her, and because her quirk allows her to manipulate it in such ways, she can also feel the ki (energy) of others, which allows her to be able to sense others. This, of course, does have its limits.

     Because the earth itself has energy, she's capable of teleporting, just like Goku and his Instant Transmission.

Here is her list of techniques, all of them in Dragon Ball Z/Dragon Ball Super terms since that's the only way she's ever heard anybody put them.

Ki Blast— The most basic form of an energy wave
Finger Beam— The user holds out their index finger and releases the energy beam from their fingertip (she does this exactly like Frieza does it, too— extends her finger, holds her hand the same way he does, and says 'bang'.)

Kamehameha

The Kamehameha is a powerful ki blast fired with two hands after concentrating a large amount of ki. There are variations to this attack that she also uses just because it's like the attacks Goku has.

Continuous Kamehameha— Multiple one-handed Kamehamehas from both hands

Bending Kamehameha— A version of the Kamehameha for which the user can change the course, allowing the user to surprise his or her opponent.

Flying Kamehameha— An aerial version of the Kamehameha

Twin Dragon Shot— A double energy sphere controlled version of the Kamehameha

MAX Power Kamehameha— A utilization of the Kamehameha in which the user uses their max power

Super Kamehameha— An advanced and more powerful version of the Kamehameha

Angry Kamehameha— A one-handed version of the Kamehameha

Kaio-ken Kamehameha— A combination of the Kaio-ken and Super Kamehameha that inflicts extreme damage depending on what Kaio-ken level is in use for the attack

Instant Kamehameha— A combination of the Instant Transmission and Super Kamehameha

True Kamehameha— A more powerful version of the Super Kamehameha.

Limitbreaker Kamehameha— A powerful variation of the Super Kamehameha

"God" Kamehameha— A powerful variation of the Kamehameha

10x "God" Kamehameha – A more powerful version of the God Kamehameha

Transcendent God Kamehameha – A more powerful version of the God Kamehameha

Instinctive Reprisal - A Kamehameha wave performed with much more energy output and force than even a God Kamehameha. Much like its original version, it can be manipulated to the user's advantage.

Supreme Kamehameha - A Kamehameha fired with far more force and intensity than the Instinctive Reprisal.

Kamehameha Blaster - A Kamehameha followed by several energy spheres.

Final Kamehameha— A combination of Goku's Kamehameha and Vegeta's Final Flash.

Spirit Bomb

Spirit Bomb – Users of the Spirit Bomb gather huge amounts of energy from all chosen surrounding life forms and inanimate objects to conduct that energy into a massive sphere of astounding destructive power.

Large Spirit Bomb – A larger and more powerful version of the Spirit Bomb, in which the energy is stored in the form of a giant light blue energy sphere in the sky.

Instant Spirit Bomb - A combination of the Instant Transmission and Spirit Bomb.

Super Spirit Bomb – A larger and more powerful version of the Large Spirit Bomb, which is directly powered by the energy of the living beings and Goku needs them to raise their hands to accumulate their energy.

Final Flash— In order to perform this technique, Vegeta draws his hands back and gathers up all of his energy. Then, he thrusts his palms forward and discharges a massive golden-yellow beam of energy towards his opponent. This is the same way Fasha uses it.

Kaio-ken— It is a technique that multiplies the user's ki for a "heartbeat" - thus increasing their power and speed and enabling them to inflict serious damage to opponents who are considerably stronger than them. However, the downside of the Kaio-ken is that it takes a heavy toll on the user's body, making them more vulnerable to enemy attacks.

Special Beam Cannon— In the anime, the move is performed by touching the index and middle fingers of one hand to the forehead and charging enough ki to attack. Its speed changes to the power level of the user performing the move. When ready, the fingers are extended forward, and two thin energy beams are unleashed from the fingers. One remains straight while the other coils around the straight beam. The resulting beam is quite powerful, drilling through most targets, and exploding on the ones it can't. So, this is how Fasha chooses to use it.

Some of her energy attacks truly are stronger than other energy attacks, it depends on how much she manages to gather. That's why she's labeled her attacks, even if they do exist in Dragon Ball Z/Dragon Ball Super. In her defense, her best friend was the one who named all of her attacks and such.