The Moon moves away from the earth - Is the theory correct ?
Okay, here goes. Because gravity falls off with distance, there is a differential in the Moon's gravity across the Earth. This differential is call a tidal force. The tidal force raises bulges in the ocean called tidal bulges. If nothing else interfered, these tidal bulges would align with the Moon.
The Earth, however, rotates. As it does so, friction between the Earth and the tidal bulges tries to drag the bulges along with the Earth. As a result, the tidal bulges lead the Moon a little. The moon tries to pull back on the bulges, but this alos means the bulges pull forward on the Moon. This transfers angular momentum from the Earth to the Moon. The Moon tries to speed up in its orbit. But doing so causes it to climb into a higher orbit and the Moon recedes from the Earth.
As far as the recession being faster when the Moon was younger, its not that simple. There are a lot of factors besides the difference in gravitational attraction. The friction between the Earth and the tidal bulges has a huge effect. Reduce the friction and the bulges lead the Moon by less and thus pull forward on the Moon less, causing a lower recession rate.
The continents play a large role in determining this friction. Because of plate tectonics, the continents weren't always in the configuration they are now. In fact, in the past they were clustered together in one landmass centered on the pole. In this configuration, they offered little resistance to the tidal bulges and the friction between Earth and the bulges is greatly reduced causing a much smaller recession rate then otherwise.