Loki used the Scepter for mind-control
Firstly, Loki did not use the Space Stone to mind control in The Avengers, it was the Scepter (within it, was the Mind stone that later ended up on Vision's forehead)
The Space Stone didn't give Carol her powers, the energy extracted from it did
Answering the second part about Captain Marvel, remember, the Tesseract (Space Stone) wasn't present during the Lighspeed engine explosion that gave Carol her powers. Mar'Vell created an energy source using the Tesseract (just like Arnim Zola and Johann Schmidt did in Captain America: The first Avenger).
The energy from the explosion of the Lightspeed Engine gives Carol her powers.
More on the Infinity Stones
We cannot predict the powers a person gets from the derived power of the Infinity Stones. Each Infinity Stone has it's own set of powers; however the powers derived/extracted/manipulated out from these stones have not been explained in the MCU: Case and point Captain Marvel's powers, and the twins' powers.
Remember, the Mind Stone (Scepter) was used to give different powers to the Maximoff twins. Wanda (Scarlet Witch) got her powers that include Telekinesis, hypnosis energy projection etc. whilst the same stone gave Pietro (Quicksilver) super-speed (Avengers: Age of Ultron).