TRUE
Yes.
Yes, cerebral dominance typically designates the hemisphere that is dominant for language. In most right-handed individuals, language dominance is in the left hemisphere, while in some left-handed individuals, it can be in either hemisphere or shared between them.
The brain hemisphere is located on the left side of the corpus collasum. This is responsible for regulating the activities on the right part of the body. Brain hemisphere is also responsible for speech and language functions.
The right hemisphere of the cerebral cortex is typically dominant in spatial tasks. It helps with tasks such as interpreting maps, recognizing faces, and understanding relationships between objects in space.
the left cerebral hemisphere
Handedness is caused by the dominance of one cerebral hemisphere over the other. Dominant right hemispheres cause left handedness (each hemisphere controls the opposite side of the body to the side it is on, since the nerves cross over). The exact reason why one hemisphere is dominant rather than the other, remains unknown. Quite possibly it is just an accident of fetal development.
The left cerebral hemisphere is typically superior in language processing, logic, and analytical thinking compared to the right hemisphere. It is also often dominant for right-hand motor control in the majority of individuals.
This is a term that generally relates to the two hempispheres of the brain, with lateralization describing the brain's tendancy to make the two hempispheres specalize in controlling different functions. (Definition courtessy of Nazia Ahmed)
If neither are Dominant Or Recessive then its called co dominance or spuedo - dominance
The word dominance is a noun. It is the state of being dominant.
Complete dominance
If by "left brained" you mean, has a dominant left cerebral hemisphere, most people have dominant left cerebral hemispheres, which is why most people are right handed (note that the left cerebral hemisphere controls the right side of the body; the nerves cross to the opposite side). In a sense, I can agree with your statement, because most people actually are terrible at writing. But it isn't their left cerebral hemispheres which are to blame. It's just that most people don't care enough about writing to learn how to do it well.