Question: Jack and Andie are brother and sister in the same grade...but does the show ever explain how that came to be? Are they twins or was Andie moved up because she is so smart?
Answer: They are not twins (Jack is older than Andie). It is possible due to when birthdays fall in the school calender for non-twin siblings to end up in the same grade. Say that you have to be 5 on Sept 1 to start Kindergarten, you are born on Sept 2, 2000 and your little sister on Aug 30, 2001. Sept 1, 2005, you are 4 years and 364 days and can't start. So Sept 1, 2006, you are 5 years and 364 days and your sister is 5 years and 1 day, and, voila!, you're both in the same grade.
Answer: The writers have said they are not twins and Jack is older. Although they were both born in 1983. In some states, like Massachusetts, it's a district decision when a child under 6-8 can start kindergarten, so there's no age deadline. In January 1988, Jack and Andie would both be 4, turning 5, and the district then allowed Andie to start kindergarten with her brother. It has nothing to do with Andie being smarter or moved up a grade, a point she alludes to in response to Jack saying he tried to start kindergarten without her (s04e04). As a side note, there was talk among the writers about whether to make Jack older or younger and they ultimately decided to make him older. The writers put in an inside joke about that when Andie says she is "definitely the older sibling in this relationship" (s04e04). It's also an inside joke to the fact that Meredith Monroe (Andie) was almost 2.5 years older than Kerr Smith (Jack). Monroe was 18, turning 19, in 1988.
Question: How does the show end for all of the characters? Who ends up with whom?
Answer: Jen dies. Joey ends up with Pacey. Dawson becomes a movie producer and produces a show based on his life.
Question: When the show started they were in the 10th grade. They graduated from the 12th grade at the end of the 4th season. Did they stay in the same grade for more than a season/year?
Answer: In seasons 1 and 2 they are in 10th grade, season 3 they are in 11th and in season 4 they are in 12th.
Answer: Yes. This is commonly done in many shows.
Answer: It's only explained once in the series. Jack says to Andie "I tried to start kindergarten without you", meaning Andie was smart enough to start school early.