As the economy matures interest rates are bound to go down, the question is not if but when. Even fund managers could get this call wrong while buying bonds.
Direct funds are still bought from the fund houses, so the fund houses will not make as much profit as before, because the TER is less in direct funds, but as of now regular funds have big share than direct funds. This gets reflected in NFOs too.
As far as the question of index investing is concerned, I cannot answer this better than this, obviously.
Regarding new entrants, not just Zerodha, here are some other applicants.
The above data can be interpreted in 2 ways - the market share being taking away from the existing fund houses or that the market is becoming bigger and the market share could remain the same if not become bigger.
We cannot predict how much of market share will be lost before someone has even begun and before they choose someone to be their RTA. All these are probabilistic in nature, and can only be analyzed when they happen.