You can typically remove about one-third of the total tree roots with no problem. This is done sometimes when trenches are cut in the soil for burying irrigation lines. But when roots are cut, about one-third of the top should be removed as well.
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Bagged steer manure was used in the past as a topdressing for lawns when overseeding. It was smelly but it worked well. Now there are commercial topdressing products available.
Spraying insecticides make mite problems more likely on susceptible plants such as Italian cypress. Miticides, unlike insecticides, are less likely to cause mite problems later.
The ground is still warm enough to plant. The magic number for landscape plant root growth is about 50 degrees.