For your system, the terms you want to use are:
Make: Toyota
Model: Corolla
Year (or "Model Year"): 2015
Plate number: AAA 123
Color: Red
Explaining why you need to use "make" instead of "brand" is harder than I expected, though. The words "make" and "brand" have the same meaning, we just tend to use one more often than the other when talking about certain types of items. There isn't always a good reason for why people use certain words.
When talking about your favorite brand of clothing, peanut butter, software, shampoo, or pretty much anything other than a car, you generally use "brand". For cars, you almost always use "make".
You would never say, "This is my favorite make of clothing".
"This is my favorite clothing-maker" also sounds a little odd.
For cars, people do sometimes say, "Here is a list of top car brands," but that could just as easily be "Here is a list of top automakers".
If asking or describing the manufacturer of a specific car, though, you definitely want make. As the text you posted points out, it just sounds odd to ask someone, "What brand is your car?" even though they would still understand you and answer the question.
Yes, these all are different words with different meanings. There are some circumstances where all three might work, but that doesn't mean all work in all circumstances.
Whereas is much more formal and is used in things like legal documents and formal proofs. It means the same as "given" or "presuming", and is really little more than a preface to some logical statement: "whereas A is true, we can conclude B".
Whereas can also be used to contrast two statements in much the same way as "but" or "however", in a more formal way: "Whereas A is true in one case, B is true in another"
Whereas the plaintiff was given many warnings about the dangers of his product, he cannot now claim he should bear no responsibility to the defendants who were injured by it.
Although is common and generally means despite or regardless of: "although* A may be true, it is not relevant to B".
Although the plaintiff was given many warnings about the dangers of his product, those dangers are inherent to its use and clearly iterated in the user manual, and the defendants should assume full responsibility for the risk.
While is common and generally means concurrent or included with: "while A may be true, B is also true".
While it is true the use of the product is inherently risky, the issue lies in the plaintiff's faulty design, not the way the product was used.
Again, there is some overlap in many contexts, because each represents similar logic.
Best Answer
The Original Poster's four examples are all grammatical. However, the sentences with there are preferable in most situations. The reason is that the phrases a car and three cars are indefinite. A car uses the indefinite article a, not the. The phrase three cars doesn't use the word the, as in the three cars. It's also therefore indefinite. This means that we haven't been speaking about the car or the three cars before.
In English we don't like to use indefinite noun phrases as Subjects. We like to put old information, stuff that we have already talked about, at the beginning of the sentence. If we put indefinite noun phrases at the beginning of the sentence, the sentence is more difficult for listeners to process.
If a sentence uses the verb BE, we can avoid this problem by using an existential sentence. We can use there is or there are. This moves the new information to later in the sentence where it is easier for the listener to process. Look at the following groups of sentences:
The sentences above are all grammatical, but they are strange and awkward. There may be some special time when want to say these sentences like this, but usually they are not a natural way of phrasing the sentence. If you generally speak like this, people will find it difficult to understand you, and they will know that your English is not very good.
If we use an existential construction instead (there is or there are), the sentences become completely natural:
Notice that the problem in the first group of sentences is that we used indefinite noun phrases. If we use definite noun phrases, the sentences become completely natural. Look at these versions of the sentences:
Those sentences sound like native-speaker sentences.
Conclusion
All four sentences are grammatically well-formed. However, the sentences with there are more natural, and will make you sound like a better English speaker. They will also make it easier for the person listening to you.