I apologize for not remembering what was in your private neuropsych. The school does not necessarily need to do additional evaluation, but it depends on the contents of the private eval. For example, many neuropsychs do academic screening only, using very sketchy (not bad, but really appropriate only for cursory screening) instruments like the WRAT. When that is the case, it is entirely appropriate for the school to offer additional achievement testing, so that all of the IDEA academic deficit areas are assessed. Something similar can happen with cognitive testing, especially as neuropsychs often pick and choose subtests to address specific functions, and may not end up with a complete battery of anything in particular. If the testing is not recent, a school may wish to re-assess all the relevant major areas of learning ability, academic achievement, executive function, and social-emotional development.
If the school has already come to an agreement that there is a qualifying disability, then, yes, you can write a 504 immediately. Also, did you have an initial IEP meeting based on the neuropsych? If so, was an extended evaluation written? This is a temporary IEP that can be written in some states, in which the team agrees that the student most likely has a qualifying disability, but additional evaluation is needed to clarify the appropriate services. The extended eval IEP usually names a specific (6 to 8 weeks, typically) deadline for reconvening to finalize the IEP. The temporary IEP allows for accommodations and some services to begin immediately on signing.
Social skills groups are kind of a grey area. I used to run social skills groups that included non-referred children (not identified with an IEP, 504, or even an ICAP/DCAP/student assistance plan). I've also facilitated lunch/friendship groups with fluid membership that included both referred and non-referred students. So hypothetically, a plan is not necessary for a social skills group. But this depends on whether the school runs groups that include non-disabled children. If they already do, then there is no particular reason either a 504 or IEP is needed for that service. If all of their groups are restricted to students identified with disabilities, then including a single student not formally identified as having a disability lays them open to citations for placing them in a special ed setting inappropriately.
