If you compare the reaction of K and H2O to other alkali metals, you will find that both Cs and Rb release more energy, and usually in a shorter amount of time.
For your second question, you must again understand that the rate of a reaction is not necessarily related to the thermodynamics of the reaction. A better comparison of the reactivities of Ag, Au and Cu is to compare the reactions of the metals and the ions of the three metals. When you do that you will find that copper metal will reduce both silver ions and gold ions, and that silver metal will reduce gold ions, but not copper, and that gold metal won't reduce either copper ions or silver ions. Therefore, we conclude that copper is more reactive than silver, which is more reactive than gold. Iron is much higher up the reactivity list, since iron metal will reduce H+ and copper, silver and gold won't.
When you compare the reactions of the metals in air, you're not even comparing the same thing. In air, iron will react with oxygen and water to make FeO(OH), which is what we call "rust". Copper reacts with the oxygen in the air to make Cu2O and CuO. Silver is not reactive enough to react with the oxygen in the air. Silver reacts with sulfur compounds in the air to make Ag2S. Silver tarnish is NOT Ag2O, it is silver sulfide. Gold doesn't react with the oxygen in the air at all. Oxides of gold are unstable, and decompose to elemental gold. Any oxide of gold is made through other chemical means, not by exposure to air.
More info: http://matsci.uah.edu/courseware/mts501/…
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I never pass up a chance to teach some descriptive chemistry. TP2010 mentions Fr as being the most reactive alkali metal. You do realize that that is in theory only. There isn't enough Fr to actually carry out such a test. Francium is the second rarest of the elements found in nature. Quantities of francium are measured in numbers of atoms rather than numbers of grams. As little as 20 to 30 grams of francium exists at any given time throughout the Earth's crust. The largest "piece" of francium contained about 300,000 atoms.
http://en.wikipedia.org/wiki/Francium