What should I do when child acts like he needs a nap?

Hi, I tutor my friend's child in math, as a volunteer, three times a week.  We'll call my friend M., and her child A.  A. has epilepsy and is ten years old.  He has been struggling in math in school since at least first grade, and I think that the school didn't know how to help him, and made things worse by getting him confused between addition, subtraction, multiplication and subtraction (and now this year they want him to exponentiate!!).  He reads well, at approximately his grade level.

I started working with him in late July.  He has made slow but good progress.  He used to do "counting on": 8 + 5 = 8, 9, 10, 11, 12, 13, using his fingers.  But because his father would hit him when he used his fingers to do arithmetic, he was afraid to actually move his fingers.  So he would lose track, and he might get 8 + 5 = 12, or 14, or who knows what.  He couldn't add, for example, 8 + 2 without either guessing a fairly randomly chosen number, or counting on, with unreliable results.

(His father no longer has shared custody, thank goodness.)

A. can now add any single-digit numbers and get the right answer most of the time.  I do sometimes have to remind him to look at his list of strategies and choose one, instead of "counting on".  We started out with one strategy (in other words, one type of addition problem), and only added another strategy when he was solid with the ones he had.

We practice in the context of a fun game similar to chutes and ladders, but with Mickey Mouse and water slides.  I flip over an index card with an addition problem on it, such as 6 + 8, and when he's figured out that it's 14, he can move his piece forward 14 on the game board.

Question 1: We've started doing skip-counting (count by 3's, count by 4's, etc.) in preparation for multiplication.  He gets lost at the same point almost every time.  4, 8, 12, 16, 20, 24, 28, 32, and then he gives me a pretty randomly chosen number -- most frequently, 34.  Any suggestions to help with this?

I have read the foundation's pamphlets, but I didn't see anything there about brain damage.  A. was tested recently by an educational psychologist and he tested extremely low on working memory.  But I read a post here on the forum that said something about brain damage resulting from seizures.  Could someone tell me more about that, or point me to a link to read about it?

Question 2: Can one recover any of the cognitive abilities that were lost?

A. takes Tegretol.  He has not had convulsive seizures since re-starting the med in early August.  Except that he has a vibration thing sometimes at night -- I don't know what to call that.  The movements are not as big as in a regular convulsive seizure.

He has absence seizures.  I think more at school and at home than with me, although I've seen at least one.

Most of the time his ability to participate meaningfully in our activity or game is good.  Occasionally it is very good, and occasionally it is quite, quite poor.

Question 3.  When it's so poor, what's going on?  Is there some sort of seizure that isn't physically noticeable, that sort of jams the proper functioning of the brain?  What should I do when that happens?

Sometimes when we go into our tutoring room after school, A. looks like he could fall asleep standing up.  One time I folded up his sweatshirt under his head while he slept on the rug, and called his mother to pick him up because I was worried about him.  That time, I wouldn't have been able to keep him awake if I had tried.  She came and woke him, about an hour into the nap.  The other time I did my best to push through with an abbreviated tutoring session, but I've been wondering:

Question 4.  Would depriving him of a needed nap risk provoking a seizure?

Question 5.  Might he have had some sort of seizure in the car on the way from school to the place we do tutoring (8 minute car ride) without showing it in any way?  My impression is that after a seizure (more substantial than a simple absence seizure, that is), the person needs to sleep.  That's was how it was when he had the convulsive seizure in early August.

Question 6.  Am I wasting my time and his trying to do our normal tutoring activities, even a shortened session, when he feels so tired?

Question 7.  A. gets a lot of headaches.  For example, perfume can trigger a headache.  I read that perceiving an annoying smell can be an aura, signalling that a seizure is coming.  Can an actual smell, that really is in the room, trigger a seizure?  Can a headache trigger a seizure?

Question 8.  Sometimes A. insists he said, or didn't, say something, or insists I said a particular thing.  If I disagree with him, he gets very frustrated and can't let it go.  Parents: what is a graceful way out of this?  Sometimes I apologize and say something like, "I guess I heard you wrong before."  But it's hard to do that over and over again!

Question 9.  If he's still having absence seizures, should we ask the neurologist if there's another medication, either to switch, or to add?

Question 10.  Might the cognitive dulling be a side effect of the Tegretol?  Does anyone have any suggestions of medications to consider?  I would not take your suggestion to an appointment and say, "We want this."  I would say something more like, "We wanted to ask you about this medication, whether it might be helpful for A."  For example, might a stimulant medication help, or Tenex (an alternative treatment for ADHD).  A. has been diagnosed with ADHD, with the dreamy type of distractibility.  He's not hyperactive.