Yes, anyone can request an IEP evaluation, but testing cannot be done without parental consent.
Second question is really testing my brain.... I know there were changes to IDEA a couple years ago in terms of initial evaluation - I don't believe SDs have the right to take that to due process anymore if you were to refuse initial evaluation.
Refusing placement? That's going to stickier, because if you refuse a particular placement, you are in effect refusing the IEP and your child loses the protections of the IEP as well as any Special Education services he may need. Then you end up with a suspended/expelled student (eventually).
Just in my experience, and how it should be, is a change in placement (which does not always mean the actual physical place, but the *services* provided - placement is programming, not geography) should be a step-wise progression, keeping in mind "least restrictive environment" (LRE). Mainstream, mainstream with- supports (up to and including 1:1 aide if appropriate), partial pull out to resource or sped classroom, sped classroom only, self-contained sped building, and the most restrictive placement would be an Residential Treatment Center (RTC). In each of those physical locations, placement would also be the "related services" as dictated by IEP team (of which you are a full member) - Occupational Therapist (OT), speech, PT, school psychiatric, transportation, etc.
The other really important point to remember is that you (or SD) can call an IEP mtg at any time. So if there is a change in "placement" and it's not working out, you request another IEP mtg (always via certified letter to sped director).
If you're contemplating refusing their anticipated proposal to move your kid to a sped classroom (which is *not* what they should be doing as a first step), I'd get an atty involved. Some SDs view segregating sped kids as their first and preferred choice. I found it very difficult to get some SDs to go through the step-wise progression of LRE. They really balk at the concept of 1:1 aides or any "related service" that is inconvenient to them - but placement cannot be for SDs convenience.