It’s very difficult to prove a negative, but I am reasonably confident that no rule in 3.5 or Pathfinder explicitly states that all armors of a given weight class slow you down by the same amount. In 3.5, at least, there were certainly a few super-heavy armors that reduced the speed by more than your typical heavy armor (Races of Stone had a couple of these).
So yes, every Medium or Heavy armor must somehow explicitly state its own speed reduction, even if the overwhelming majority of them have the same speed reduction. On the other hand, if a given case failed to do so, I’d just chalk that up to the designers not realizing there was no such general rule, since it usually is so consistent and armors which slow people more or less than others in their category are quite rare. It’s also worth keeping in mind that it is consistently weight category that we should consider, not sheer weight.
There's no such thing as total round movement. Your speed is how far you move when you take a move action.
The simplest move action is moving your speed.
(from the CRB combat section on actions)
The haste spell increases your speed(s) in an overly complicated manner, which nonetheless states:
All of the hasted creature’s modes of movement (including land movement, burrow, climb, fly, and swim) increase by 30 feet
(source: Haste spell text in your post)
A typical character has a land speed of 30 ft. Increasing that movement mode by 30 feet results in a land speed of 60 ft, because 30 + 30 = 60 (source: addition).
When a creature with a land speed of 60 ft. takes a simple move action, it moves 60 feet (see above). If said creature elects to use a second move action at a later time, that character would again move 60 feet. After two move actions, the character would have covered a total of 120 feet, because 60+60=120.
If said character instead elected to take the 'run' action, the character would instead move three or four times their speed (depending on if they have the run feat or not), and that would result in a total movement of 180 or 240 feet respectively (source: multiplication).
Best Answer
Yes (for your own) and no (for mounts & devices):
Armor changes the movement speed of the one wearing the armor, as soon as it does encumber at all. So on this case, it is yes, you get a reduced movement speed on all of your movement ratings unless you have a feat that spares you of those.
However, keep in mind several classes have a good chance to be mounted on a being that can have other movements while in heavy armor (like a Chevalier or Paladin on a Pegasus or a Druid on a Roc). Unless the ride wears a fitted armor (barding), it will move with its own movement speed, only accounting you if you get too heavy. So no you don't account your armor on your mount's movement rating (but keep in mind it adds to your weight). Barding has the very same movement reduction as the table you referenced to - light barding doesn't hinder, but medium and heavy prevent fly speeds as of their own rules.
And then there are objects, like a magic carpet. These usually say if they work with overload and what their altered speed would be - again, it is not the armor worn by the operator, but its weight that could reduce the speed. Others like the Crab-spider-submarine don't state weight limits, in those cases, one might assume they operate at their top speed no manner how much is in them (but GM can also enforce a limit under Rule #0).