Colleges typically use your best scores from each section of the SAT, even if they're from different testings, so it can't hurt to re-take the tests.
If she recently took the PSAT, she should have received THREE scores (Math, Critical Reading, and Writing). Each of these scores should have been in double digits--between 20 and 80 (e.g., 46 or 58 or 62, etc.) with the highest possible total at 240 for all three sub-sections.
Are those scores good? That's largely in the eye of the beholder. I would certainly call them "good" but not "great." They are at or above the median range at many fine colleges and universities and below it at others (e.g., the Ivies and their equivalents).
If your strongest academic areas are those not tested by the SAT I (e.g., foreign language, science, history) then it might make the most sense for you to try to do extremely well on the SAT IIs in January. This will enable you to apply to a broader range of colleges and also will help offset your crummy SAT I. (Chances are, if you scored really badly in October, it's not going to improve a whole lot in three months anyway.) On the other hand, if your SAT I was really a disaster (perhaps you misnumbered your answers?), it might be worth retaking.
Frankly, I don't agree with your counselor. Your son should not send very poor scores to colleges that do not require them.
You should definitely take the World History SAT II this year. It's always a good idea to try the SAT II as soon as you've completed the corresponding course, assuming that you won't be taking a more advanced version of it later on.
Each time you take the SAT I or II, your scores will be sent to the colleges and/or scholarship services you indicated on the registration form at the time you signed up to take that test. They will also go to any additional colleges or scholarship services you have requested after you registered. These schools will receive the scores for that particular administration along with scores from all SAT I and SAT II you have completed in the past.
Most admission folks are fairly forgiving when it comes to freshman and even sophomore foibles, especially when standardized tests are "stellar" and the applicant has excelled in tough courses in grades 11 and 12.
The university probably got your name from "Student Search." If you checked the appropriate box when you registered for the SAT, you gave the College Board permission to release your name and address to subscribing colleges. Colleges and universities pay for the Student Search service to help them locate students with the characteristics they're seeking.
No, you don't have to take the Test of English as a Foreign Language (TOEFL). Occasionally students in your situation will do so because they think that having a high score will work in their favor at admission-decision time. However, as you can imagine, admission officials simply ignore such results because they don't consider English to be a second language.