www.alphadictionary.com

Consider the following sentences:

There was a heated argument, as often happens.
We disagreed, as is often the case.
The answer is as follows.
Think what will happen if we fail, as seems possible.
As was customary, they sat on the floor.

Is 'as':
(a) a pronoun acting as the subject of the dependent clause, or
(b) a subordinating conjunction, or
(c) both?

What is the terminology for the 'as' in things like, "His face was red as a beet."? "His face was red, as beets generally are."? These feel different to me somehow, though I can't put my finger on it.

For a tiny little two-letter word, we expect "as" to do a lot of work. The dictionaries say it can function as an adverb, a conjunction, a preposition and a pronoun.

Audiendus and Slava post the following sentences for our consideration, numbered here for our convenience.
1) There was a heated argument, as often happens.
2) We disagreed, as is often the case.
3) The answer is as follows.
4) Think of what will happen if we fail, as seems possible.
5) As was customary, they sat on the floor.
6) His face was red as a beet.

In my opinion, in 1), "as" is a relative pronoun meaning "which." The antecedent is "argument"
In 2), "as" is an adverb meaning "in the way expected"
3) is not a complete sentence in my opinion. It should be
3a) The answer is as follows: . . . .
Here, "as" is again an adverb modifying the verb "follows." Some sources suggest "as follows" is itself an phrasal adverb.
In 4), as in 2), "as" is an adverb meaning "in the way (to be) expected."
In 5) "as" is a conjunction meaning "because" or "since."
in 6) "as" is a conjunction meaning "equality of condition." I believe 6) as stated by Slava is a reduction of
6a) His face was AS red AS a beet. Many dictionaries cite "as A as B" as an example of conjunctive use of "as."

Thanks a lot. I have a few further comments/questions:

In my opinion, in 1), "as" is a relative pronoun meaning "which." The antecedent is "argument"
I would prefer to say that the antecedent is the whole of the clause "There was a heated argument". So we can say: "There were heated arguments, as often happens".

In 2), "as" is an adverb meaning "in the way expected"
So what is the subject of the second clause? "The case"?

3) is not a complete sentence in my opinion. It should be
3a) The answer is as follows: . . . .
Here, "as" is again an adverb modifying the verb "follows." Some sources suggest "as follows" is itself an phrasal adverb.
(a) "The answer is as follows" looks like a grammatically complete sentence to me, except for the usual problem of the "as".
(b) If "as" is an adverb, what is the subject of the verb "follows"?

In 4), as in 2), "as" is an adverb meaning "in the way (to be) expected."
So what is the subject of "seems"? It cannot be the phrase "what will happen if we fail", because that belongs to a different clause.

In 5) "as" is a conjunction meaning "because" or "since."
What is the subject of "was customary"?

in 6) "as" is a conjunction meaning "equality of condition." I believe 6) as stated by Slava is a reduction of
6a) His face was AS red AS a beet. Many dictionaries cite "as A as B" as an example of conjunctive use of "as."
Yes, some dictionaries class the first "as" in the "as...as..." construction as an adverb (meaning "equally"), and the second "as" as a conjunction (with an implicit verb at the end, e.g. "as red as a beet is").