How fast will they grow?
The answer here depends on you. If they are given excellent care, which means effective weed control, water if needed in the first year (and second if in very dry climates), and fertilizer on time, both hazels and chestnuts can grow "fast". Their tops will make 1-3' for hazels and 2-4' for chestnuts in the first year, 3-5' for hazels and 5-7' for chestnuts in their 4th year. They will grow faster after the first few years of root establishment.
However...All our hybrids at Badgersett are selected for survival in neglect, because neglect is very often the reality they must face. Everyone puts tree plantings in with the best of intentions of taking good care of them, but the real world—in the form of broken legs, car accidents, weddings, divorces, bulls getting through the fence, etc—has a way of intruding. Then the plants don't get taken care of. Nobody coddles the trees in the woods, after all, so these little trees probably will be fine... Our trees will survive anyway, but their visible growth will be minimal for several years. What they will do if neglected, with no weed control and no fertilizer, is put every scrap of energy they can glean into the root system, not into the visible top. So it is possible to come back to a planting after 3 years of neglect and get the impression that the plants are not growing at all. Not so. Once the roots reach a critical stage, the plants will start to push the top growth fairly rapidly. This may happen at age 3-5 years, depending on just how tough their life has been.