How common do schools superscore SAT and ACT scores? And for the ones that do, do you know if they only look at the superscore or do they also consider the highest composite?
It's hard to generalize about superscoring. That said, I will proceed to generalize about it.
It seems that colleges more often superscore the SAT than the ACT. But first, a short explanation of superscoring...
[Superscoring is the practice of pulling the highest score in each SECTION of the test, and creating an independent composite score.
For example: Student X took the SAT in June and received a 600 in Math, 570 in Reading, and 690 in Writing for a total score of 1860 in that sitting. He retook the test in September and received a 620 in Math, 520 in Reading, and 720 in Writing for a composite score of 1860 for the second sitting. If a college superscored the SAT, then student X's composite would be 1910.]
Here's an outside blog post that explains superscoring in the context of the ACT, and also includes a list of colleges that superscored the ACT in 2008. If you do use this list, make sure to contact or reasearch each college you're interested in to confirm that their policy has not changed.
As for the SAT, the College Board publishes this PDF, which includes an exhaustive list of colleges and their score policies. While this information is published directly by the College Board, it is still a good idea to confirm score policies on a college's website or through e-mail contact.
I'm not 100% on the second part of your question. As I understand it, the highest composite would be your superscore, and the superscore would take precedent over any single sitting.
I do know that taking the SAT more than a three times is generally considered frivolous.
On that note, students rarely improve upon a 2nd SAT sitting (statistically speaking). The College Board includes with your scores the average improvement of students in your score range taking the SAT a 2nd and 3rd time. This information can give you insight into the value of retaking the SAT.