Will a full earth illuminate the lunar landscape more than a full moon will illuminate surface of the earth

Earth's surface area is 15 times that of the Moon, and the albedo is 5 times greater (35 versus 7). Therefore you answer

Yes, quite a bit.

The Earth, seen from the Moon, is 3.67 times larger. Therefore its visible disk will cover 13.5 times more area in the Moon's sky, than the Moon covers in our sky.

Also, the Earth is more reflective than the Moon. The Moon reflects only 12% of the light it gets (on average, the Moon's surface is as dark as a freshly paved, ashphalt parking lot -- without the yellow lines)
The Earth reflect 37% of the light it gets. That is 3 times more reflection.

3 times more reflection over an area 13.5 times bigger = 40 times more light.

Full Earth will give you 40 times more light than the Full Moon gives us on Earth.

Enjoy the trip.

Absolutely.

First, the albedo of the Earth (the amount of the sun's light it reflects) is 0.39 - 39% of the light. Second, the Earth is quite large - 4 times the diameter of the moon, and 16 times the reflective area.
The moon's albedo is only 0.07, and with is much smaller than the Earth - limiting further the amount of light it's able to reflect.

Idk, I would say ask an Apollo astronaut but they were only there during the lunar day time.