L.R.
I have been through it all on this subject so here it goes:
1. There are two different tests for classical and gifted schools. The classical schools test measures what your child knows/how academically advanced they are (math, reading and language arts). The gifted test measures how they think (analogies, patterns, etc.). My daughter scored 97th percentile last year on the classical test and did not get in. That is because she was competing for one of ten spots at Decatur, so they probably only took kids at the 99th percentile, or scores in the top 1%. So, to answer your question, these schools are very selective - it's really hard to get in. Things have changed this year. CPS has dropped the consent decree, which used to require that two-thirds of the kids they accepted were of any ethnicity. This year, 50% of the kids they accept are top scorers, regardless of ethnicity. The other 50% is divided into four groups using socio-economic criteria based on the census tract in which you live. They will take the top scorers within those four groups. Had my daughter taken the test this year, she would have been competing for one of 18 spots (a slight help). If you get lucky, you might enter in a year where they take two kindergarten classes instead of one, so that would also double your chances.
2. This year they have changed admissions criteria for magnet schools and I believe they are giving preference to siblings. Theoretically, at gifted schools, they give preference to siblings in the neighborhood program (many of the gifted schools have neighborhood programs in the same school), but they take neighborhood kids first. If the classes fill up with kids from the neighborhood, you are out of luck.
3. Living within district does not improve the odds of getting into a gifted program. For instance, if you live in the Coonley school district (Coonley is a regional gifted center with a neighborhood school under the same roof), your child would still have to test into the gifted program, and you are competing against kids from all over the city. However, you would be guaranteed a spot in the neighborhood program. If you are talking about a magnet school like Hawthorne (unlike gifted schools, admission to magnet schools are not test-related), I believe they have changed admissions criteria so that a certain percent of kids are from the neighborhood. This does not guarantee you a spot, but improves your odds.
Hope that helps. It's really complicated and took me several months to figure it all out. Good Luck!