Good instruments for dysgraphia and disorders of written expression include the TOWL-4 and the PAL-II. For younger kids with fluency/motor issues, I would lean toward the PAL-II, as it has measures of fluency and automaticity. (The PAL is only normed through elementary school, so you can't use it with older kids.)
OT and practice will not make dysgraphia go away, but it might remediate enough to provide better access to some handwritten tasks. The question of emotional impact will vary depending on the child, the clinician, the severity of the disability, and the strength of the compensatory mechanisms. You know your child best.
Depending on the nature of the fine motor, visual, or perceptual weaknesses (and although the Beery is technically in the Average range, it is apparent that something is going on from the extreme fatigue when writing), other accommodations might involve decluttering or organizing visual materials, e.g., by reducing the number of items on a page, using visual frames and guides, providing large square paper for math (to help line up numbers for accurate computation).
