When i make a payment on my red card the amount is credited the next day and available for use. sometimes it takes a day or two for TD bank to pull the payment from my checking account. As far as the debit, i believe it works like any other debit card, your available balance is available for use.
I don't know the answer to your first question, but as far as debit being accepted for payment, I kind of doubt it. At least at Best Buy when I worked there, payments were cash only. I'd assume it's the same for Target.
