1. When walking on wet grass on shabbos, you place your already wet shoe on grass and thereby give some watering to that grass, so why is it permissible to walk on wet grass?
2. If when opening the Succah roof, water will drop onto the lawn, is this permissible on Shabbos and Yom Tov.
Answer:
1. There is no problem of walking on wet grass on Shabbos. The principle reason for this is that the grass is already wet, and the possible transfer of moisture from one area to another has zero effect, so that this cannot be considered "watering."
Even if you will be walking on a dry patch, no prohibition is involved because there is no certainty that moisture will be transferred, so that even if moisture is transferred (to the degree that can benefit the dry grass -- not a likely story) and this is therefore not a pesik reisha but rather a davar she-eino miskaven, which is permitted.
2. Opening the roof so that water will fall on the lawn is a problem where the lawn has already dried off a little, or where the rainfall was not strong so that the lawn is not saturated with water and will benefit from the additional water.
Under these circumstances (where the lawn will benefit from the added water) one must be careful to take off the cover in a manner that the water will not fall directly onto the lawn. This will be similar to the halachah of washing one's hands over a lawn, which is prohibited on account of the prohibition of watering.
Under most circumstances, the roof is only drawn onto the Sukkah during a heavy rainfall, and removing it will be permitted because the added water will not make a difference to the lawn.
Best wishes.