What are the problem we may face if there is no rotation and revolution
Answers
So, what you are asking for is a static Earth relative to the Sun? No movement?
Okay. There is one face of the planet always facing the Sun. In relation to the other planets and objects in our solar system, Earth is held in place while all other planets still revolve around the Sun.
Number one, most life on the surface of the planet would develop and congregate around the terminator. That is the line between light and dark on the planet, where the Sun shines all the time, and it never shines. The reason for this is that we never evolved to live in daylight all the time. Our circadian rhythms would never have developed. Our lives would depend on having some degree of protection from full sunlight so that we don’t dehydrate or suffer from sleep depression.
Food crops would die in areas of full sunlight. Too much sun would bake them, and evapotranspiration would not be able to keep up to keep plants at a temperature lower than surface ambient.
Weather would suck! The temperature differential between light and dark sides would create whirling vortices that would dwarf hurricanes and tornadoes. The winds would be moving across the planet in an attempt to stabilize the atmospheric temperature. It would be deadly hot on the light side, and freezing cold on the dark side. Perhaps not cold enough to freeze the atmosphere, but cold enough to freeze the ocean on the dark side.
There would be no tides as we know them. There would be a permanent bulge of water toward the Sun. This would have the effect of flooding areas that now are dry, while leaving many seacoasts dry. Eventually the Earth would have an egg shape, with the pointy bulge pointed at the Sun.
We would lose our Van Allen belt which now protects us from cosmic rays and x-rays. The molten outer core would not be flowing, although it would remain molten. That movement of iron-rich molten rock is what creates our magnetic field, so compasses would also no longer point to north. The loss of the Van Allen belt would mean that life on Earth would be imperiled by solar radiation. Life dies. The radiation belt also protects the atmosphere, which would be deteriorated slowly but surely by cosmic rays until the solar wind drove the gasses away from the planet entirely.
Death.
Earth would become an obstacle in the solar system. Anything revolving around the Sun in the path of the Earth would strike it at tremendous speeds, at least 67,000 miles per hour which is our current speed around the Sun. Impacts from asteroids, comets, the Moon, would eventually destroy the planet. The constant bombardment would fracture the Earth, and although gravity would try to hold it together, nothing would prevent the fracturing of Earth. We would become another asteroid belt .