I want to redo the lawn in the backyard because it had too much weed, moss,
and the ground does not slope away from the foundation enough (my crawspace
gets wet).

The plan is to till the soil, add compost, add a french drain, regrade the
slope and then reseed the lawn.

After killing off the existing lawn, I found that under the surface it is
crisscrossed with tree roots up to 2-inch in diameter. They appear to come
from a birch tree in the corner. I yanked out some of those roots and have
some more to go. Other than cutting down the tree, is there a way to prevent
the roots from invading the lawn in the future?

Also, the soil seems very clay-like. In fact, when it rains some puddles
would form and drain away very slowly. Should I do something about this,
like add sand?

Some books suggest the french drain be put near the foundation wall. I fear
that losening the soil near the foundation would weaken the support of the
foundation, so I'm inclined to put the french drain on the perimeter of the
lawn, i.e. the lowest point after it is regraded. Would this work?

-peter