Я не мог поверить, что всё это правда.

Because the sentence is in the past tense.

• могу = I can / I am able
• мог = I could / I was able

The verb is мочь = to be able to / can. In the past tense, Russian uses forms that also show gender:

• мог = masculine
• могла = feminine
• могло = neuter
• могли = plural

So Я не мог поверить... tells you the speaker is masculine. A female speaker would say Я не могла поверить...

Because Russian usually places negation before the finite verb, and here the finite verb is мог.

So:

• Я не мог поверить = I couldn’t believe
• literally: I was not able to believe

This is different from:

• Я мог не поверить = I could have not believed / I might fail to believe

That version changes the meaning. So in your sentence, не мог поверить is exactly the normal way to say couldn’t believe.

Because поверить is perfective, while верить is imperfective.

Here is the difference:

• верить = to believe, to have belief, to trust, as an ongoing state
• поверить = to come to believe, to accept as true at a particular moment

In this sentence, the idea is not general belief. It is the moment of mentally accepting something as true. So:

• Я не мог поверить... = I couldn’t believe...
• more literally: I couldn’t bring myself to accept that it was true

If you said не мог верить, it would sound more like I couldn’t believe/trust in an ongoing sense, which is not the normal idea here.

Here что means that and introduces a subordinate clause.

So the structure is:

• Я не мог поверить = I couldn’t believe
• что всё это правда = that all this is true

Russian что can also mean what in other contexts, but not here. In this sentence it is a conjunction, not a question word.

Because Russian normally puts a comma before a subordinate clause, and что всё это правда is a subordinate clause.

So the comma marks the boundary between:

• main clause: Я не мог поверить
• subordinate clause: что всё это правда

This is very standard in Russian punctuation. Russian uses commas in places where English sometimes would not.

Всё это means all this or all of this.

Why всё?

• всё = everything / all of it / the whole thing
• все = all people / all items in a plural group

Here the speaker is referring to the whole situation as one thing, so всё is the right form.

A useful contrast:

• всё это = all this
• все эти люди = all these people

Also, the letter ё matters here. In many texts Russians write все instead of всё, but the meaning here is clearly всё.

Because Russian usually omits the verb to be in the present tense.

So:

• Это правда literally = This truth
• actual meaning = This is true / This is the truth

Likewise:

• всё это правда = all this is true

If the sentence were in the past or future, Russian would normally use a form of быть:

• Всё это было правдой = All this was true
• Всё это будет правдой = All this will be true

But in the present tense, the is is simply understood.

In Это правда / Всё это правда, правда is a very common predicate word meaning true or the truth.

So:

• Это правда = That’s true / It’s true / It’s the truth
• Всё это правда = All this is true

Why not правдой?

In present-tense sentences like this, Russian often uses the nominative form for predicate nouns in fixed, common expressions such as это правда.

The form правдой is instrumental, and you often see it with an explicit past/future form of быть:

• Это было правдой = It was true

So in your sentence, правда is exactly the natural form.

Russian word order is fairly flexible, so yes, you can sometimes move things around.

Your sentence:

• Я не мог поверить, что всё это правда

is a very neutral, natural way to say it.

A version like:

• Я не мог поверить, что это всё правда

is also possible. The meaning is basically the same, but the focus shifts slightly. The original всё это groups the idea as all this. The alternative can sound a little more like that this is all true.

So the original is probably the best basic version for a learner to remember.

Only the past-tense form of мочь changes:

• masculine: Я не мог поверить...
• feminine: Я не могла поверить...

This is because Russian past tense agrees with the speaker’s gender in the singular.

Everything else stays the same:

• Я не могла поверить, что всё это правда.

So if you see мог, the speaker is masculine; if you see могла, the speaker is feminine.