Yes, both PS5 and PS4 games can be stored there. The only difference is that PS5 games stored on the external HDD must be transferred to the console's SSD in order to be played. It's fair to say that this external drive can be used as an archive drive only.

As already answered several times, PS5 games can also be saved. To play them, however, they must first be moved to the internal memory.
No, there is no external hard drive for PS5 games. However, you can expand the internal SSD memory for PS5 games (M.2 SSD).