1. You never know. However, a lot of words are reused often and you can just google, "common SAT words" to get a list of them. Still, your reading score will probably only improve 10 points for every 100 words you learn. If you combine studying vocabulary with practice tests to learn how to do well on the reading comprehension part, you can gain a lot more points though. The ACT doesn't test vocabulary.
2. The math is pretty much basic algebra and basic geometry. By that, I mean, you should be able to convert word problems to algebraic equations, you should know certain things about shapes (180˚ is the sum of the angles in a triangle). Most of the math covered by the SAT is learned in 6th grade to 9th grade. For the ACT, you should know about trigonometry.
3. The grammar covered in the SAT and ACT is pretty basic grammar. It's mostly subject-verb agreement and pronoun-antecedent agreement. You also should know about misplaced modifiers. Just google those topics and you should be able to break 700 with some practice.
4. Know the definition of the word "refute". Odds are you'll see that come up in either a reading comprehension question or a vocabulary question. Also, look up the other common words.
5. Usually there are local, independent SAT/ACT tutoring organizations that you would have to look around for in your area. Also try to see if there is a local "Test-Takers," "Princeton Review," or "Kaplan". Those are larger organizations that tend to really help students raise their scores.
6. Take lots of practice tests and after you take them, attentively go over your wrong answers. With time, you will pick up on the mindset that will lead you to the correct answer for each type of question. It takes a lot of practice tests, but usually something will just click for each section, and your score will suddenly jump (I jumped from 1980-2040 on each practice to getting 2120-2150 on each practice to getting 2230-2280 on each practice without ever being in between each interval)
7. Bring a watch to put on your desk on test day. It is much quicker to check that, then look all the way up at the room clock.
Drink tea or Gatorade Focus before the test. They both contain amino acids that stimulate the brain's focus and keep your body relaxed.
Use a slightly dulled pencil, because there is more surface area, and it is much faster to fill in the scantron.
For a single passage on the reading section, circle all of the answers in the book before transferring them to the scantron. You keep your mind on the passage more and it keeps you more focused. For everything else though, fill in the bubbles as soon as you know the answer that way you don't run out of time.
Good luck!