Assuming no buffs or any other helpers,
how does swimming speed compare to running speed?
Is there any other environment that may make the player character move slower or faster?
Yes, swimming is slower than normal running. (WoWpedia claims it's about 2/3 the speed, although it certainly feels slower.) Also, regular movement speed buffs don't apply when swimming, only swim speed buffs.
Aside from water and other things you move through, there are no terrains that naturally change your speed. However, an area can put a passive or temporary buff on you that changes your movement speed. For instance, the tar pits in Cataclysm-era (modern) Un'Goro have a debuff that makes you move and swim much slower. On the other hand, the faction towns in the Vale of Eternal Blossoms have a buff that increases movement speed in the main shrines. These effects are visible like other buffs.