A1:Here's my take -- I think that the intent is twofold: 1) keep people from abusing the movement/action economy (within the given context, that is); 2) a nod to verisimilitude.
1) Without the "no 5-ft step" restriction, you'd be able to take a full-round action and still move 5 feet -- that isn't really fair to the guy that is using his movement .... "hey, the guy who took his full-round action is still able to move half as far as the guy who dedicated his round to moving" or "WTF - using a free action to do the same thing that requires a move action" Also, consider this from the SRD:
In some situations, your movement may be so hampered that you don’t have sufficient speed even to move 5 feet (1 square). In such a case, you may use a full-round action to move 5 feet (1 square) in any direction, even diagonally. Even though this looks like a 5-foot step, it’s not, and thus it provokes attacks of opportunity normally. (You can’t take advantage of this rule to move through impassable terrain or to move when all movement is prohibited to you.)
You can’t run or charge through any square that would hamper your movement.
2) typically, a 5-ft step is basically considered to be rather effortless and is simply done in the course of everything else you do in that round. If the fog is so restrictive on your movement that it takes an entire move action to simply move 5 feet, then it doesn't really make since that you can move the same distance effortlessly.
A2:Yes, you are still restricted:
If you occupy squares with different kinds of terrain, you can move only as fast as the most difficult terrain you occupy will allow.
I know that that particular sentence says "terrain", but I think that the overall intent is clear (i.e., when you take in the entirety of the movement rules)