Learn Hardcore Icelandic: Hann keyrir rólega.

Both. Icelandic simple present often covers habitual and right-now actions, so it can mean either “He drives slowly” or “He is driving slowly,” depending on context. If you want to make the ongoing action explicit, you can say Hann er að keyra rólega (“He is driving slowly right now”). Note: vera að can also mean “about to” in some contexts, but with activity verbs like keyra it usually means “is doing (now).”

Why is it rólega and not rólegur?

Because rólega is an adverb modifying how he drives. Rólegur is an adjective and would describe the subject, not the manner of driving.

Hann er rólegur. = “He is calm.”
Hann keyrir rólega. = “He drives calmly/slowly.”

What’s the difference between rólega and hægt for “slowly”?

rólega literally means “calmly, gently,” and in everyday speech it also covers “slowly.” It hints at a relaxed, unhurried manner.
hægt (from hægur, “slow”) zeroes in on speed.
Examples:
Hann keyrir rólega. = He drives calmly/slowly (relaxed manner).
Hann keyrir hægt. = He drives slowly (low speed). You’ll also hear the set phrase hægt og rólega = “slowly and steadily.”
Note: hægt can also mean “possible” in other contexts (Það er hægt = “It’s possible”). Context disambiguates it.