Can I download games on hard drive, then transfer them to my xbox series x ?

Not really...

Xbox Series X games / upgrades / updates has to be installed onto the Series X internal or expansion card SSD,

You can have Xbox One games on your external hard drive that will get an Series X upgrade but the games will need to be transferred to the Series X and then the Series X upgrade will need to be downloaded onto the Series X SSD,

As an example...

I have Marvel Avengers on my external hard drive that will get the Series X upgrade and I will transfer the game over to the Series X SSD ready to download and update the game to the Series X version when available.

If the games are Series X optimized, you will need to transfer them to the internal hard drive on the Series X in order to play them, but as Obsessive Power stated, you can just plug the hard drive in and not have to redownload anything.

yes you can play all your games from your hard drive you can plug a 3.0 hard drive in to the new xbox series x and can copy xbox series x games to the hard drive but you will need to copy them back to the xbox if you want to play them again

What about the games that I currently have stored on my external hard drive? Will I be able to use that on my Series X to play those games? Or will I have re download them on the Series X?

Hi,

Current external hard drives are USB 3.0 5,400 RPM mechanical hard drives. These drives are very slow compared to the Expansion card. You won't be able to run Series X/S games from current external hard drives, not even the 2.5" external SSD drives either.
But, you will be able to archive your Series X/S games to these drives to save downloading again.

The expansion card can run all compatible Xbox games. Which will be Series X/S, Xbox One and the BC Xbox 360 and original Xbox games on the BC list.

Xbox One and other Backwards compatible games will load a lot faster on either the internal storage or the expansion card than they would if you ran them off your external hard drive.

Microsoft has a video on YouTube showing 'The Outer Worlds' loading in just 11 seconds on a Series X/S SSD, compared to nearly 60 seconds on Xbox One.

https://www.youtube.com/watch?v=_wCX0n9Jci4

I see. So how would i be able to transfer everything i have on my old hard drive to the new expansion card?