Chehkov-liszt,
Because your child is being evaluated partly to see if he has disabilities that are interfering with his education, your child has some protection under the IDEA. If you disagree with the results of your school's evaluation, they have to pay for you to have an independent evaluation with the evaluator of your choice, provided that your evaluator meets the general requirements (licensure in your state, etc) to conduct the kind of evaluation you are asking for, or they have to go to court to prove that their evaluation was correct. Your request for an IEE should be in writing. You do not have to give a reason why you disagree, although you will almost certainly be pressed to do so. Check out
Wrightslaw and read through the copy of the Procedural Safeguards that you were given by the school. If you don't still have your copy, they will provide you with another one.
As for your other questions -
Have you had his vision thoroughly evaluated (not the screenings at the school or pediatrician's office)? Problems with convergence are often worse close up, and the computer reading distance is usually further away than desk. Also, in most computerized tests, there is only one question presented at a time, so the "page" is less distracting and less visually confusing. The text size might also be larger, or the contrast might be different. All of these factors can make a difference in how easy the test is to read on computer vs. on paper.
You've also noted that your son has been diagnosed with writing issues, and the handwriting component is absent on a computerized test, so that probably helps him focus on the actual material rather than having to struggle with writing to get his answer out correctly.
Something else to consider is that some of this might be related to the other issues you already I'm know that you are dealing with. I'm not an OT, but if you are seeing an OT who is trained in Sensory Integration issues and retained relfexes, you can double check what I am saying here. My son's OT told us that many kids with SI dysfunction also have retained infantile reflexes which can interfere with academic performance in a number of ways. For example, if your son has a retained ATNR or STNR, looking down at the desk or trying to look back and forth from a book to a paper, etc., can be very difficult because of the reflex reactions that make it hard to focus and that make the child move in their seat, or that make the hand jerk a little bit every time the head turns a little. The computer screen doesn't require these head movements, so your son might have an easier time concentrating with that format. (A retained palmar grasp, STNR, or ATNR can also impact writing significantly.)
Just some things to think about.
Good luck.