Is this possible to focus common light (not laser) to a small point in the wall and control it with mirrors?

"A common light" needs to be defined better. I assume you want to use an incoherent source such as an LED or an incandescent light. The size of the smallest spot to which a light beam can be focused depends on the size of the light source. Imagine, for example, trying to focus light from the Sun to a small spot. In essence, this means forming a small image of the Sun. If you study how a lens works (e.g., this figure from Wikipedia illustrating the geometry of image formation by a lens), you'll see that the angle from the lens to the two sides of the image is the same as the angle from the lens to the two sides of the Sun.

A smaller spot can be formed from sunlight only by imaging a smaller portion of the Sun. So, in order to form a small spot from an ordinary incoherent light source, with the spot at a distance from the lens, you would need a source that is extremely bright and extremely small. There really is nothing that easily fits the bill. A diode laser works fine, but is coherent and therefore not "ordinary".

An alternative to consider is to use a strong light source for example halogen lamp, which is typically used in fiber optic illuminator.