The investigation is apparently at an "advanced" stage, so the SEC must have been looking into their relationships with high-speed trading firms long before that suicide happened.
Supposedly they are looking at a $10 million fine, which is a drop in the bucket compared to the $200 million they just raised in another round of seed funding. It will make for a rough quarter for Robinhood whenever they settle the case, but I'm sure they made much more than $10 million selling their customers' orders to these firms. Now they basically just need to pay a fine and put something in the fine print about it.