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We don't see any particular symptoms that look concerning; most are likely either slight environmental stress (from the plants still establishing) or more minor leaf-spot infections that tend to be common this late in the growing season. Treatment isn't needed (and wouldn't be effective after the appearance of symptoms), but you can dispose of the fallen leaves later this autumn in case it helps reduce levels of any overwintering spores.

In your first foliage close-up photo, the small black pellets are frass (a term for insect poop), and suggest that a caterpillar or other insect may be chewing on the foliage. The runny black streak a few photos down is also probably from a caterpillar or other insect which was squished or fed-upon by a bird, spider, or predatory insect, or killed by an insect-specific disease. Few leaf-eating insects on walnut are gregarious and capable of consuming large volumes of foliage (and if present here, they would be quite noticeable on such a young tree), so this is probably a lone feeder and not one to be concerned with. Trees, even those this young, can afford to loose some leaf tissue so close to their normal shedding period in autumn.

The mulberry leaf spots could be a different disease than what's impacting the walnuts, but here too, treatment is not warranted or effective, and the issue is probably not serious.

Keep up your routine of checking them for water regularly as we move into autumn; you can slow or cease this checking once the surface soil starts to freeze since dormancy will greatly slow the plants' water use by that point. Some autumns, we have experienced quite dry stretches, which is why maintaining root hydration is important to lessen the risk of bud damage. Try to feel the soil around five or so inches down before watering to determine if the soil is dry enough to need irrigation; you may find, especially as our nights begin to cool, that you can reduce the watering frequency, though soaking each time is good to make sure the moisture seeps in deeply enough. In general, if the soil feels moist about five inches down, you shouldn't need to water yet. Rains will, if course, impact this interval, but bear in mind that relatively short, albeit heavy, rains don't always saturate the soil. Though this isn't necessarily the cause of leaf browning here, over-watered roots can succumb to dieback and cause some desiccation damage to foliage (such as marginal or tip browning and crisping) as a result, so it's just something to be aware of for the future. Overall, the plants seem to be in decent shape, and vigorous growth is a good sign of roots that are probably healthy.

Miri