Using an external HDD to play games

So, I'm looking at getting some more space (shocker, I know) and I was wondering if the Seagate Ultra Slim Backup Plus 2TB or 4TB would be an option. I'm using that Google Express Groupon to buy it from Costco, and I have two questions:

1) Would either or both be an option for simple plug, format, and play? Meaning, out of box I could format, download games, and play from the external HDD.

2) Would either or both be able to be dismantled and installed into my PS4 if external is not an option.

Having trouble finding this info. Any help is appreciated. Thank you!

Link to HDD that I'm looking at

Edit: It seems the 4TB is not the "Ultra Slim" model. Still looking at it, though.

Here is the Costco link