Learn Hardcore Indonesian: Saya dapat mengerti materi presentasi dengan mudah. - I can understand the presentation material easily.

Yes. You can also say Saya bisa mengerti materi presentasi dengan mudah.
In the sense of “can / be able to”, dapat and bisa are usually interchangeable.

dapat sounds a bit more formal or written.
bisa is more common in everyday spoken Indonesian.

So your original sentence is slightly more formal than the bisa version, but both are correct.

Is dapat mengerti redundant? Doesn’t mengerti already mean “to understand”?

Mengerti by itself means “to understand,” but dapat/bisa + verb is a very common pattern to express ability or possibility: dapat mengerti = “can understand / be able to understand.”
It isn’t considered redundant; it adds the same nuance English has between “I understand” and “I can understand.”
With dapat, you emphasize that you are able to understand it (for example, because it’s clear, well‑structured, not too difficult).

Can I omit dapat and just say Saya mengerti materi presentasi dengan mudah?

Yes, that’s also correct and natural: Saya mengerti materi presentasi dengan mudah.
Without dapat, you’re simply stating the fact that you understand it easily.
With dapat, you highlight your ability or the possibility of understanding it (often implying that the presentation is not too difficult).

Is another word order possible, like Saya dapat dengan mudah mengerti materi presentasi?

Yes, this word order is also correct: Saya dapat dengan mudah mengerti materi presentasi.
Indonesian word order is fairly flexible with adverbs like dengan mudah.
Your choices include:

Saya dapat mengerti materi presentasi dengan mudah.
Saya dapat dengan mudah mengerti materi presentasi.
The meaning is the same; putting dengan mudah earlier can slightly emphasize the easily part.

What exactly does materi presentasi mean? Is materi like “material” in English?

Yes, materi here is very close to English “material” in the sense of content / subject matter.
Materi presentasi usually refers to what is being presented: the topics, points, explanations, slides content, etc.
It’s usually treated as a mass noun, so you typically don’t need a plural form like materi-materi in this context.

Why do we use dengan in dengan mudah? Could I say something else to mean “easily”?

Dengan mudah literally means “with easy,” but it functions as “easily”, an adverb of manner.
You can also say, for example:

sangat mudah = very easy
mudah sekali = extremely easy
gampang sekali (more informal)

You cannot just drop dengan and say *Saya dapat mengerti materi presentasi mudah; that sounds wrong. You need dengan mudah or another structure like materi presentasi itu mudah untuk saya mengerti.

Is dengan mudah an adverbial phrase? Where can it go in the sentence?

Yes, dengan mudah is an adverbial phrase of manner. It can appear in several positions:

Saya dapat mengerti materi presentasi dengan mudah.
Saya dapat dengan mudah mengerti materi presentasi.
Dengan mudah, saya dapat mengerti materi presentasi. (more emphatic / written style)

All of these are grammatical; the differences are mostly about emphasis and style.

Could I say Aku instead of Saya? When should I use each?

Yes, you can say Aku dapat mengerti materi presentasi dengan mudah.

Saya is neutral to formal, and safe in almost all situations, especially with strangers, teachers, colleagues, or in writing.
Aku is informal/intimate, used with friends, family, or people your own age when the situation is casual.

In a classroom, talking to a teacher or in a formal presentation, Saya is the better choice.

Is mengerti formal or informal? I’ve heard people say ngerti.

Mengerti is the standard and correct form, suitable for both spoken and written Indonesian.
In casual speech, people often shorten it to ngerti:

Aku ngerti materi presentasinya. (informal)
Use mengerti in anything formal or when you want your Indonesian to sound standard and clear.

What’s the difference between mengerti and memahami here?

Both can often translate as “to understand.”

Mengerti is very common and covers general understanding.
Memahami tends to suggest a deeper, more thorough understanding, closer to “to comprehend / to grasp in depth.”

In your sentence, you could say Saya dapat memahami materi presentasi dengan mudah, which sounds like “I can easily grasp/comprehend the presentation material,” possibly implying a bit more depth.

Can dapat here ever mean “to receive” or “to get”?

Not in this sentence. With the pattern dapat + verb (mengerti), dapat clearly functions as a modal verb meaning “can / be able to.”
Dapat can mean “to get / to receive” when it stands alone or is followed by a noun, for example:

Saya dapat materi presentasi. = I got/received the presentation material.

But in Saya dapat mengerti…, there is no such ambiguity.

How would I say “I can’t understand the presentation material easily”?

You can negate it with tidak before dapat:

Saya tidak dapat mengerti materi presentasi dengan mudah.

More natural alternatives (depending on nuance) include:

Saya tidak bisa mengerti materi presentasi dengan mudah.
Saya tidak begitu mengerti materi presentasi. (I don’t really understand the presentation material.)

Do I need to change anything in the sentence if I want to talk about the past or the future?

No. Indonesian doesn’t change the verb form for tense.
You keep Saya dapat mengerti materi presentasi dengan mudah, and add a time word if needed:

Tadi saya dapat mengerti materi presentasi dengan mudah. = Earlier I could understand the presentation material easily.
Besok saya pasti dapat mengerti materi presentasi dengan mudah. = Tomorrow I will definitely be able to understand the presentation material easily.