"If the first distribution of interest rates have occurred does it mean it has started (accruing) 30 days ago?"

As far as I know, it should start accruing when the interest rate began at the new percentage. But don't quote me on that.

"Also, does it distribute daily?"

Again, as far as I know, it distributes monthly. But even if it distributed daily, it wouldn't make a difference because the balance wouldn't be adjusted, so there's no compounding taking place.

[EDIT] - To clarify...

The interest doesn't "distribute" daily or monthly. It just accumulates continuously and can be effectively claimed no more than once every 30 days. So the only compounding that can take place is monthly.