You are definately doing something wrong...
Have you read the preparation tutorial?
start on http://www.truefresco.com/technique

>After my frescos are finished, dried, etc., I
>notice they cannot get wet; the pigment will
>smear...

This will only happen if you apply paint after the plaster have already set. It might look wet but it has already "gone off". Depending on the skill and "correctness" of the application it should not happen for atleast 2-14 hours after it (plaster) was layed.

>In fact, the putty will soak up a lot of
>moisture and get soft.

You did mix sand into the putty, did you? Even if you did not this should not happen.

>Doesn't the pigment and
>putty turn to stone and become impermeable?

This is correct - you can wash frescoes with scrubbing brush and soap and pigment should not smear.

>Is
>there a curing time for a finished fresco in
>which it will turn to stone.

About 500 years, but in a month you should not be able to "knock" them (frescoes) of the wall without the jack hammer.

>My friend wants me
>to make fresco tiles as part of the splash board
>behind her sink in the kitchen. Aren't there
>frescoes outdoors on the sides of cathedrals and
>the like?

You are right frescoes are often ysed out doors and it is not a problem for the plaster to get wet - just like stucco. However I would not suggest using them for the splach board due to salts, detergents, etc....

Do post the detailed description of the way you have painted yours so I can poin out the problem areas in your experiments.

ilia