A total solar eclipse occurs when the Moon passes between the Sun and the Earth, blocking the Sun's light and casting a shadow on a portion of the Earth's surface. During this phenomenon, the Moon appears to completely cover the bright disk of the Sun, resulting in a temporary darkening of the sky.
To answer your second question, during a total solar eclipse, the shadow of the Moon can indeed fall on Earth without any part of the Moon touching the Earth's surface. The Moon's shadow consists of two parts: the umbra and the penumbra. The umbra is the central region where the Sun is completely blocked, and the penumbra is the outer region where the Sun is only partially obscured.
For a solar eclipse to be considered a "totality," the entire disk of the Sun must be covered by the Moon from the perspective of a specific location on Earth. In other words, the observer must be within the path of totality to witness a complete blockage of the Sun. The width of the path of totality varies for each eclipse but is typically around 100 miles (160 kilometers) wide. Within this path, the Moon's umbra touches the Earth's surface, and those within it experience the full darkness of totality. Outside this path, in areas under the penumbra, a partial solar eclipse is visible, where only a portion of the Sun is obscured.