Qi is a form of internal force that allows changes in a person's body, allowing the use of combat arts and enhanced training for warriors.
Mana is a external power that is derived from the understanding principles of the world around someone, mana allows mages to shift and warp natural phenomena around them to their will. Its is used in almost every conceivable field and every one can use it, but some people are better at it then others.
Chaos energy is a precursor to both mana and Qi and can be used to replenish both. But Chaos energy by nature is extremely volatile, and tends to destroy most things it comes into contact with. It also has the tendency to corrupt entities and objects that are infused with it into chaos beings or chaos tools.
These three energies do not interfere with one another. some one can easily use mana and Qi.