Το ότι η απάντηση αργεί τόσο πολύ με γεμίζει αγωνία.

Yes, ότι means that, but το ότι is a very common structure meaning the fact that.

Here, το turns the whole ότι-clause into a noun-like unit:

Το ότι η απάντηση αργεί τόσο πολύ = the fact that the answer is taking so long

That whole clause is the subject of γεμίζει.

So structurally, the sentence is:

[The fact that the answer is taking so long] fills me with anxiety.

Because η απάντηση is the subject of αργεί inside the embedded clause.

In other words:

• η απάντηση = the answer / the reply
• αργεί = is late / is taking a long time

So η απάντηση αργεί means the answer is taking a long time.

It is not the object of anything here, so it stays in the nominative.

Αργεί comes from αργώ, which often means:

• to be late
• to take a long time
• to be delayed

With η απάντηση as the subject, it means something like:

• the answer is late
• the answer is taking a long time
• the reply is delayed

So it does not mean that the answer itself is slow in a physical sense; it means it has not arrived yet, or is delayed.

They work together as an intensifier.

• πολύ = a lot / very / much
• τόσο = so / that much

So τόσο πολύ means so much or so long, depending on context.

Here, with αργεί, it gives the idea of:

• is taking so long
• is delayed so much

You could hear just πολύ in other sentences, but τόσο πολύ is stronger and more emphatic.

No. Here με is the weak object pronoun meaning me.

So:

• με γεμίζει = fills me

This is easy to confuse with the preposition με meaning with, but here it is not a preposition.

A very literal breakdown is:

• με = me
• γεμίζει = fills
• αγωνία = anxiety

So: it fills me with anxiety.

Γεμίζω literally means to fill.

In this sentence, the subject is the whole clause:

Το ότι η απάντηση αργεί τόσο πολύ

and the verb is:

γεμίζει

Then:

• με = the person affected (me)
• αγωνία = what I am filled with (anxiety)

So the structure is basically:

[something] fills [someone] [with a feeling]

Greek often uses γεμίζω this way with emotions:

• με γεμίζει χαρά = it fills me with joy
• με γεμίζει φόβο = it fills me with fear
• με γεμίζει αγωνία = it fills me with anxiety

Because αγωνία is being used as an abstract noun in a general sense.

Greek often leaves out the article with abstract nouns when the meaning is general:

• χαρά = joy
• φόβο = fear
• αγωνία = anxiety

So με γεμίζει αγωνία means it fills me with anxiety in a general, emotional sense.

If you used an article, it would sound more like a specific, identifiable anxiety:

• την αγωνία = the anxiety

But here the meaning is broader and more natural without the article.

Because the subject is not several separate things. The subject is one whole idea:

Το ότι η απάντηση αργεί τόσο πολύ

A whole clause used as a subject is treated as a singular thing, so the verb is singular:

• το ότι ... γεμίζει
• not γεμίζουν

You can think of it as:

This fact fills me with anxiety.

And this fact is singular.

Yes, Greek word order is more flexible than English word order.

The sentence as given is natural and straightforward:

Το ότι η απάντηση αργεί τόσο πολύ με γεμίζει αγωνία.

But Greek could also say:

Με γεμίζει αγωνία το ότι η απάντηση αργεί τόσο πολύ.

That version puts the emotional result first for emphasis.

So the original order is not the only possible one; it is just a neutral, very natural arrangement.

Because Greek is describing a current, ongoing situation.

• η απάντηση αργεί = the answer is taking a long time
• με γεμίζει αγωνία = it fills / is filling me with anxiety

Greek often uses the simple present where English may prefer a progressive form:

• Greek: αργεί
• English: is taking a long time

So the present tense here does not mean a timeless general truth; it describes what is happening now.

In some contexts, πως and ότι can both introduce a that-clause. But in this specific structure, το ότι is the standard expression meaning the fact that.

So here το ότι is the natural choice.

A learner should probably treat το ότι as a fixed and very useful pattern:

• το ότι... = the fact that...

That will help you recognize similar sentences quickly.