How can I use Card Order?

Yes, this is consistent and you can use that information to help you play.

For example did the player junk their whole hand at mulligan (less likely to have a killer opening), or keep the whole lot? Did they keep their whole hand but not play it on the first few turns (pieces of a combo maybe)? Did they consider playing a card then play a different one (might that be a spell if they tried to target something first)?

There are programs like Deck Tracker that will do this for you, giving details like which turn they drew it on, whether it came from another card (like duplicate or a discover card), but it is entirely possible to do it all in your head, if you're good at keeping track of things like that.

It can be very powerful to finesse your choice of play, but it's only a little piece of the puzzle, so you still need to think through your turns and consider all possible plays, but it helps to gauge risk.

You can use this to gauge whether or not your opponent has high-curve cards or answers to your threats. If they've been holding something since the beginning of the game, it's likely a late-game threat. If you played a big minion and they removed it with the card they just drew, it's more likely that they were not already holding an answer - perhaps a signal that they may not be able to deal with another big minion.