I have always had the policy to never use a debit card for online purchases. Ever. If they overcharge you they have your money right out of your account, there is no credit card company with a stake in it that you can complain to about fraud and the bank doesn’t care, has no skin in the game and will just say “Can you prove it wasn’t legit? We have no way, your word against theirs” and do nothing.
I don’t practice purchasing on line and if I need to (funerals etc.) I use a credit card.
I always tell people to never use debit cards. As you noted, the money is taken from your account, and even though you can typically get it back, it’s gone until you file for it.
A credit card, in the other hand, offers much better fraud protection, and it’s not your money on the line until you pay it. Of course, one needs some discipline when using credit, but if you can pay the amount off each month, credit cards will save you money.
Additionally, you are paying for credit card use whether you use them or not, because the merchant fees are a business expense. These fees, typically a couple percentage points, are included in the item prices. So you might as well use a reward credit card if possible (assuming you pay it off regularly).
We once had both our credit and debit card numbers stolen at the same time (I assume a bank leak as we never used both cards at the same vendor). The credit card was turned off immediately by the credit card company when their algorithm detected a suspicious charge, while the fraudsters made several debit card transactions before I had to call the bank to turn that card off myself. That was it with debit cards for me.
BTW, I followed up with the vendors on the fraudulent charges. They were made in my name, but nothing else matched (obvious fraud). The purchases were shipped to an address in New York—not my state, obvious buyer/shipping address mismatch—to a person with a common Taiwanese last name, something like Cheng. I even found the house in Amazon street view, but I bet nothing ever happened to the thief. I did eventually get the money back in my account.
Re: 6 - Great points!