I deposited money into the brokerage's account at the failed bank just before it collapses (T+1), for settlement of a trade. Is there a problem?
This must be considered by the administrator of the failed bank based on the actual situation.
What settlement alternatives are available? For instance, should I take cheques directly to the brokerage?
Yes, you may take cheques directly to the brokerage for settlement. You are advised to clarify with your brokerage directly for other settlement alternatives.
I have in my possession a cheque drawn by the brokerage on the failed bank. Can I still bank in the cheque?
You should ask the brokerage to make other alternative arrangement.