Grammar Explanation: Why Use ‘a’ Before ‘Elements of a First Step’?

The original version of the sentence was correct:

I have Sodium and Potassium.

This type of element (i.e. elements considered to be metals)...

Sodium and potassium are a single "type of element" (considered to be metal), despite being more than one element, so "element" should be singular.

Even if your list was many longer, it would still be a single "type of element":

Sodium, lithium, potassium, rubidium, cesium and francium are the "alkali metals".

This type of element is defined by ...

If, instead you had:

I have sodium and potassium, which are metals, and helium and neon, which are noble gasses.

This is when you get to pluralize, and you would make both parts plural.

These types of elements...

The two "types" here are "metals" and "noble gasses".

The same is true with your other examples:

He prepared some french fries and insomnia cookies, assuming that this type of (crispy) snacks would fit my appetite.

In this example, there's still only one type of snack... crispy, so this should be written:

He prepared some french fries and insomnia cookies, assuming that this type of snack would fit my appetite.

And:

I am recently addicted to Triumph of Death and Tessellation; when I listen to this type of (metal) songs, I feel alive.

There's only one type of song... metal.

I am recently addicted to Triumph of Death and Tessellation; when I listen to this type of song, I feel alive.

Now, to add to this, it's not uncommon in actual use to find examples with mixed singular and plural forms like your example. Right now, I'd say they're ungrammatical but whether they remain ungrammatical could be considered to be in flux.

For the time being, if you make sure to ask yourself, "How many types are there?", you should be able to be sure to use the correct form.

This earlier question addresses your issue as well:

Types of things vs. types of thing

And here's another one that might help:

“Types of” followed by singular or plural?

I don't know what you know.

The sentence is ambiguous in terms of its meaning because it's ambiguous in terms of its syntax too.

It is possible that the string what you know is a fused relative here (a special kind of relative clause construction sometimes also known as a free relative). In this case the string what you know is a noun phrase. It represents an entity. These kinds of fused relatives with what can be paraphrased using the words the thing(s) that. We can paraphrase the fused relative reading of the sentence (and make it slightly clearer by adding the word same) like this:

• I don't know the same things that you know.

In this reading of the sentence we can consider the simple object of the sentence (as opposed to the full grammatical object of the sentence) as the pronoun what. This word represents the actual thing which is unfamiliar, unknown, to the speaker.

Alternatively, the string what you know could be read as an interrogative clause. In this case, if the you concerned was called Bob, for example, the sentence would mean something like:

• I don't know the answer to the question: What does Bob know?

[I used Bob in the sentence above because the deixis of you could cause further problems here]

Here the whole interrogative clause what you know represents a question, the answer to which is unknown to the speaker.

Grammars like The Cambridge Grammar of the English Language give detailed analyses of the different structures of fused relatives and interrogative clauses. The most pertinent difference is that—according to their analysis—in the fused relative reading what you know is a noun phrase (a phrase headed by a noun or pronoun, in this case the word what) , whereas what you know in the interrogative reading is an interrogative clause (and therefore ultimately headed by a verb, in this case the verb know).

There is a nice test you can do, which will tell you whether an item is a fused relative or an interrogative clause. In the interrogative clause reading you can add the word else after the what and the sentence will still make sense and still be grammatical (although it will have changed its meaning somewhat). So the following sentence can only have the interrogative reading:

• I don't know what else she knows.

The sentence above can only mean:

• I don't know the answer to the question: What else does she know?