Can we say that birch is autotroph during the day and heterotroph at night?

Birch is a plant. Almost all plants, with rare exceptions, are autotrophs, because organic compounds in them are formed from inorganic ones. This process is called photosynthesis. It needs light, because it is then that the chlorophyll pigment is active. Photosynthesis consists of light and dark phases. The latter also takes place during the day, it just does not need light.

Photosynthesis stops at night, but this does not mean that the plant becomes heterotrophic. It does not consume ready-made organic matter, but absorbs minerals from the soil.