If I was to buy a booster for a month, lets say the 1000 tc one. Does the tc amount cap to the 100 games as the qi? Or can you do more than 100 games a day?

Above that, if I was to do lets say the 100 games a day by shoveling in a public room I would get 3M in a month, would that be ok? Or what is the limit where its considered "illegal farming"

yes, i believe the tc still caps at 100 games a day.
2nd question, probably okay. depends on how fast you get 100k a day.

If you wanted to play joust 100 times a day for a month it would be okay. But I'm sure if you won 95% of the games you played in a month that would bring up questions

I don't see how legitimately winning matches can be considered farming.