You can pay your medical bills however you want. Your HSA provider gives you a debit card linked to your HSA account for convenience only. You request reimbursement from your HSA provider, and hang onto all receipts in case you are audited by the IRS. You must report all HSA deposits and withdrawals to the IRS when you file your taxes each year. There's no need to submit receipts to your HSA provider...whether your withdrawal is taxable or not is between you and the IRS only.

Also, as far as I know there is no deadline for when you must request reimbursement by. I pay my medical bills on a points-earning credit card and leave my money in my HSA account where I can invest it in stocks. I save all my receipts (and scan them for storing electronically). I plan to request reimbursement many years down the road after my money has earned interest over the years.