So far I have,
How do you deal with slippage?
What are your margine requirements?
How do you handle margin calls?
Do you charge commission or interest rates?
Do you credit or debit rollover interest rates?
Is there anything I am missing?
“[U]By whom and where are you regulated[/U]?”
It’s hugely important.
You find out how good a broker is, in ways that really matter, [I]when something goes wrong[/I].
For myself, I would never open an account with any broker and transfer funds there without first checking their [B]regulatory record[/B].
And if several different regulators have made adverse rulings against them and fined them multiple millions, repeatedly, [I]for matters arising directly over the way they’ve treated their clients[/I], then I would [B][U]run[/U][/B] (even in these shoes).
I think Customer Support of any broker could give you answers. Some of them are check-able on any broker site.
I would add: “How can I deposit / withdraw money and are there any specific requirements here?” and “Is it possible to modify / open / close a trade over the phone if I cannot access my account for any reason?”
Also as bengi suggested such basic questions should be easy to answer from the broker’s customer support 
Yeah, I am in contact with several brokers and I’ve been messaging them my original questions. I wanted to see if there were any additional questions I could ask.
You guys provided excellent additions. Thank you!
Do you keep clients’ deposited funds in separate bank accounts to your own capital?
(though I think in a well regulated jurisdiction (see lexys’ post above) this will be a standard requirement). Don’t be tempted by any cut-price offer from a firm based at a postcode in some tiny new island nation.
I asked my broker about “what is your clearing house”.
You could “Do you offer any bonuses?” and have in mind that if the answer is positive, then you should be extra cautious as these kinds of brokers are not so trustworthy. You can also check if they have any requirements for minimum and maximum deposit, do they have a Dealing Desk and what type of orders does their trading platform offer.