1. KTEA-II or WIAT-III would be my picks. Do not do the WIAT-II; it's outdated. The WJIIIACH tends to generate slightly inflated scores for very young children, but some might view that as a plus.
2. Yes. Make sure you get all components of math, including math reasoning/problem solving and math calculations/numerical operations. Math fluency is not important at this age.
3. I'm not familiar with NJ, but operating on general principles based on the parts of the USA with which I have experience, I would imagine, yes, if you submit a parental request letter with a clear statement of the likely educational needs that you are trying to identify. Maybe someone from NJ has more info on this? I did find this FAQ on the DOE website:
http://www.state.nj.us/education/genfo/faq/faq_gandt.htm
