Yes they are.
Yes, as said above even sale prices.
Pretty much once you sign in you get the local price but not all items are online or in store
You have to sign into your account online @Costco to check the member prices in some cases
Can't say for sure. Most seem close, but because of shipping costs they may not be exactly the same. Of course remember that you can return items at the store that you got from Costco online. If buying gifts for out of town family, I usually buy online -- it's easier and cheaper than trying to pack and ship it myself!
Yes even the sale items
Thanks! Your answer is awaiting moderation.