Learn English – “I could meet you” vs “I can meet you” & “I would meet you” vs “I will meet you”

This is not gramatically correct, no.

"a" implies a noun, e.g. "person," "woman," "worker."

"You are a selfish [type of person]" would work, e.g. "You're a selfish man, aren't you?"

If you do not want to use a noun (because, for example, you don't know what kind of person they are because you are talking over the internet) you can instead write "You're selfish, aren't you?"

I could not find anything better than this on Dictionary.com

It says that 'for' in such context has been used as a conjunction meaning 'because, since'. It's old usage of the word 'for'.

[Middle English, from Old English; see per in Indo-European roots.]

Usage Note: 'For' has been used as a conjunction meaning "because, since" for over 1,000 years. It is familiar in many famous quotations, from the New Testament's beatitudes (Blessed are the meek: for they shall inherit the earth, Matthew 5:05) to Shakespeare's sonnets (For thy sweet love rememb'red such wealth brings / That then I scorn to change my state with kings).

Today this use of for is rare in speech and informal writing, and it often lends a literary tone or note of formality. · Like the word so, for can be viewed as either a subordinating or a coordinating conjunction, and it has been treated variously as such. It has the meaning of a subordinating conjunction, since it clearly subordinates the clause that follows it to the previous clause or sentence. But like a coordinating conjunction, for has a fixed position in the sentence, and its clause cannot be transposed to precede the superordinate clause containing the main idea. It is ungrammatical in present-day English to say For they shall inherit the earth: blessed are the meek. Perhaps because of this ambiguity in function, for is treated variously with regard to punctuation. Sometimes it begins a dependent clause and follows a comma, and sometimes it begins an independent clause (as if it were a conjunctive adverb like moreover) and follows a semicolon or period (when it is capitalized as the first word of a new sentence). All treatments are acceptable in standard usage. The difference is really one of emphasis: starting a new sentence with for tends to call more attention to the thought that it introduces.

So,

I didn't go to school today for I felt ill.

is not weird because you want to say that you did not go to school today because/since you felt ill.