Capitalization in quotations

I suppose this is not a repeated question.

While it's natural to capitalize the first letter in a quoted sentence (even it's split into two parts), I want to know should I capitalize the first letter of quoted vocabulary (such as a noun, or something more special) which shows up at the first place. e.g.

(Each of the following is a complete sentence.)

(Of course, there're plenty of alternative expressions.)

"red" is a concept of color.

or

"Red" is a concept of color.

More specially, what about

"a2b7x" is the code I got.

(Capitalizing "a" would just give a wrong code.)

and

The sentence started without capitalization, reads as "i start with a lowercase 'i'".

The punctuations and the capitalization rules are there to serve the purpose to carry information explicitly and accurately. So I think that forms are less important than content/meaning and we may allow the existence of sentences such as

"a" is a lowercase letter.

It's really strange to say

"A" is a lowercase letter.

After some clarification in comments under the question, what's essentially being asked is if there are situations where you can start a sentence with a lowercase letter.

This is a matter of style, and different people and style guides will give different guidance. There is no universal rule that would be violated if you did start a sentence with a lowercase letter, but most main style guides recommend that it not be done.

From The Chicago Manual of Style, 8.4 [paywall]:

… Most editors will draw the line at beginning a sentence with a lowercased name and choose either to rewrite or to capitalize the first letter for the occasion. When a personal name includes a lowercase particle, the particle is capitalized if it begins a sentence or a note …

Chicago qualifies this even further in 8.154:

Brand names or trademarks spelled with a lowercase initial letter followed by a capital letter need not be capitalized at the beginning of a sentence or heading; the existing capital letter is sufficient to signal that these are proper nouns. Likewise, names that begin with a capital letter and include additional capitals in the middle of the word should be left unchanged. (In either scenario, such capital letters are sometimes referred to as intercaps or midcaps.) Chicago draws the line, however, at names in all lowercase; in order to signal that such a term is in fact a proper noun, an initial capital should be applied even midsentence …

      iTunes is both an app and a media service.
      Does your iPhone have an AccuWeather app?
      PowerPoint has become virtually synonymous with presentation software.

With respect to quotations, Chicago mentions that it's acceptable to silently change a lowercase letter to an uppercase letter in a quotation (or vice versa), if doing so would make it fit the syntax of the surrounding text.

From 13.19:

When a quotation introduced midsentence forms a syntactical part of the sentence …, it begins with a lowercase letter even if the original begins with a capital.

      Benjamin Franklin admonishes us to “plough deep while sluggards sleep.”

      With another aphorism he reminded his readers that “experience keeps a dear school, but fools will learn in no other”—an observation as true today as then.

When the quotation has a more remote syntactic relation to the rest of the sentence, the initial letter remains capitalized.

      As Franklin advised, “Plough deep while sluggards sleep.”

      His aphorism “Experience keeps a dear school, but fools will learn in no other” is a cogent warning to people of all ages.

On the other hand, for a quotation that is only a part of a sentence in the original but forms a complete sentence as quoted, a lowercase letter may be changed to a capital if appropriate. In the example that follows, “those” begins midsentence in the original …

      Aristotle put it this way: “Those who are eminent in virtue usually do not stir up insurrections, always a minority.”

            but

      Aristotle believed that “those who are eminent in virtue usually do not stir up insurrections, always a minority.”

Based purely on this guidance, and acknowledging that other style guides and personal styles can differ, the following is what Chicago would recommend with respect to the sentences in the question:

1. "Red" is a concept of colour.
   
   Whether "Red" is a common noun or proper noun, the first letter should remain, or be changed to, a capital.
   
   

2. The code "a2b7x" is what I got.
   
   The sentence has been rephrased. If a2b7x were a regular noun, it would start the sentence with A2b7x8, where the lowercase a become an uppercase A. However, in this case, since it's a code, which is most likely case sensitive, the case of the letters cannot be changed without changing the code's literal use. Because the case should not be changed, the sentence has to be rephrased so that the lowercase version isn't at the start of the sentence.
   
   

3. … reads as "i start with …"
   
   The third sentence in the question should include "i start with" and use a lowercase i. As with the second sentence with the code, it's referencing something explicit where the case needs to be maintained.
   
   I have not actually written the entire sentence out here, however, because it involves style decisions far more complex that what have been discussed so far. The mix of quotation marks, words as words, and punctuation, all combine to make it exceedingly difficult to effectively style. It would most likely need to be rephrased to at least a small degree, and at least some of the quotation marks removed in favour of using italicized text.
   
   

4. The letter "a" is a lowercase letter.
   
   The sentence has been rephrased, as with the second sentence. Neither of the suggested variations in the question would work. The first would fail because the sentence starts with a lowercase letter (one that doesn't exist as part of a word with an uppercase letter), and changing the case would alter the intended meaning too much. The only option is to rephrase the sentence.

But at the risk of being too repetitive, let me repeat that this is not a universal rule. There is no universal rule for this. While what I've given is common guidance, it's not the only way of approaching the situation.