Does Robinhood hold custody of the bitcoin I buy from them? Do they have the private keys? Or does someone else hold custody. Thanks!
Robinhood says they keep all coins in their custody, yes. See here:
Unfortunately, you can't actually withdraw coins from Robinhood, even though the coins are supposedly held in their custody (not derivatives). It's strictly an investment platform where they hold all assets. Supposedly, cryptocurrency deposits and withdrawals are coming in the future.
I actually just mentioned that to strengthen my point that you do not own the bitcoins, if you do not have sole access to the private keys. This was one of the reasons why I did not want to use this service, because Robinhood is just shifting numbers around in their own internal database and you will never own the bitcoins/assets that you bought.
I doubt that withdrawals will be implemented in the near future, because you do not have to own any bitcoins if you manage your own internal ledger.