Ive been watching my cousin play toribash for a while and im not too bad, i just had a question on what QI is. I know its used as a restriction in the market but how does one earn it? Thanks

QI is the number that represents the number of games you have played (100 QI= 100 games played) As you said, QI is used as a restriction in the market, so if you have high QI ou can buy more expesnive items. Also, there is a 100 QI limit per day. You can still play after 100 games, but you wont gain QI. You can buy QI: click here
Or you can buy QI boosters, that double the QI you gain: click here
QI also determines your belt:

Belt chart

Show

---

WhiteBelt ------------------- 0-19
YellowBelt ------------- 20-49
OrangeBelt -------------- 50-99
GreenBelt --------------- 100-199
BlueBelt ----------------- 200-499
BrownBelt -------------- 500-999
BlackBelt ------------- 1000-1999
2nd Dan BlackBelt -- 2000-2999
3rd Dan BlackBelt -- 3000-3999
4th Dan BlackBelt -- 4000-4999
5th Dan BlackBelt -- 5000-5999
6th Dan BlackBelt -- 6000-6999
7th Dan BlackBelt -- 7000-7999
8th Dan BlackBelt -- 8000-8999
9th Dan BlackBelt -- 9000-9999
10th Dan BlackBelt - 10000-14999
Master Belt ---------- 15000-19999
Custom belt --------- 20000-49999
GODBELT ---------------- 50000+

Godbelt
-_-
Then one belt 100,000
Then elite belt 1,000,000
at 3mil qi your qi resets

No one has EVER gotten to 3mil QI though. How would we know?

-_-
It's how the QI system was made.

Question: If I double my QI gain does it double the QI limit per day?

What do you mean 'double my qi gain'

If I buy the Qi Booster X2, which "[...] allows the subscriber to gain belts and Qi twice as fast."

the qi limit stays the same

Technically, yes, it does
Sinse it doubles the qi gain, you gain double the qi you would normally get. But no, it doesnt let you play 200 games and get qi from them