When opening a corporate account, do online brokers normally require that the owner(-s) will be personally liable, if the account end up below zero?
I have no idea about trading accounts, but it is very common for personal guarantees (PG) to be required on business accounts for such things like bank accounts, creditors, vendor services, etc. If you have enough business credit history and/or are of large enough size, those requirements are often waived.
First you open an individual account with a broker and then after showing a track record of a year or two you can open an LLC account and negotiate to get the personal guarantee removed. You can get that done with about $1M cash in the LLC account.