I deposited a cashier's check into my account at 8AM, the account had nearly nothing in it. If I were to use the "credit" option on my debit card at the grocery store would I overdraw my account? Do the "credit" transactions on my debit card go through immediately? If I were to write a check instead, and they didn't cash the check today, would I be safe?
The bank will know best. You could look for their documents on the website that discuss funds availability. The size of the check could also make a difference.
One way to see if you can use the money is to look online at your balance. My credit union reports two numbers for each account: Balance and available balance. The difference covers the deposits that are in limbo, and the checks/withdraws that are in in progress.
There does not seem to be a relationship between credit/debt status with the debit card and the speed of the withdrawal. I have seen it take seconds, and I have seen it take days. It depends on the vendor.
regarding the use of a check. If you were mailing the check you would probably be OK, because of the time it would take them to receive it and process it. But handing the check to the store might not be any different than using a debit card. Many stores are now scanning the check into the system, then handing you back the paper check. that can be deducted within minutes of handing them the check.
While it seems that the cashiers check is as good as cash, there have been scams using cashiers checks. Your bank may not treat it as good until there has been time for the other bank to verify it.
Generally, checks that are deposited, are being put on-hold for a couple of days (or more, depending on the amounts) until the amount is available. But they do post on the date deposited, and usually some initial amount ($200 in my bank) is available right away. The amounts and holding periods change from bank to bank, so ask your bank. Usually, when you check balances online, it would show the amount available. If the check you wrote gets to the bank before the full amount is available it may bounce.
Cashier checks are not exactly like cash. Since there has been a lot of fraudulent activities involving cashier checks, many banks treat them as regular checks for most parts, including holding periods.