Learn Hardcore Russian: Эти заметки помогают мне видеть, что моё продвижение идёт медленно, но достаточно успешно. - These notes help me see that my progress is going slowly but quite successfully.

Literally: These notes help to-me.
The thing that helps is in the nominative (эти заметки), and the person being helped is in the dative (мне).

How does the construction помогают мне видеть work? Is this like help me to see in English?

Yes. Russian often uses помогать кому-либо делать что-либо:

помогать
- кому? (dative) + что делать? (infinitive)

Here:

помогают – they help
мне – me (dative)
видеть – to see

So помогают мне видеть is directly parallel to help me (to) see.
This pattern is very productive:

Он помогает мне понимать русский. – He helps me understand Russian.
Они помогают нам учиться. – They help us (to) study.

Why is it видеть and not увидеть here?

The choice is about aspect:

видеть – imperfective: to be in a state of seeing, to see in general, continuously or repeatedly.
увидеть – perfective: to manage to see, to notice once, to see as a completed event.

In this sentence, the speaker talks about an ongoing ability:

помогают мне видеть, что… – they help me (in general / regularly) see that…

If you used увидеть:

помогают мне увидеть, что…

it would sound more like help me (finally / at least once) realize / notice that…
That would emphasize a one-time realization, not a continuing awareness. The original stresses an ongoing perspective on the progress.

Why is it моё продвижение, not моя продвижение?

The possessive pronoun must agree in gender, number, and case with the noun продвижение.

продвижение ends in -ие and is neuter in Russian: оно, моё, твоё.
So you must use моё (neuter), not моя (feminine).

Forms of мой in nominative singular:

masculine: мой план
feminine: моя идея
neuter: моё продвижение

So моё продвижение literally means my progress / my advancement, with both words in nominative neuter singular.

What exactly does the noun продвижение mean here, and why use a noun instead of a verb like я продвигаюсь?

Продвижение is a noun meaning:

progress, advancement, moving forward (literally or figuratively).

In this context it is abstract progress, like progress in learning or work.

Russian often prefers a noun + идёт for abstract processes:

работа идёт хорошо – the work is going well.
ремонт идёт медленно – the renovation is going slowly.
моё продвижение идёт медленно – my progress is going slowly.

You could say:

Эти заметки помогают мне видеть, что я продвигаюсь медленно…

That is also correct and natural. Using моё продвижение makes the sentence a bit more formal/abstract, focusing on the progress itself as a thing, rather than on me moving forward.

Why is идёт used with продвижение? It literally means goes, right?

Yes, идти literally means to go / to walk, but in Russian it is also widely used with abstract nouns to mean to progress / to proceed / to be happening.

Common patterns:

дело идёт хорошо – the matter is going well.
урок идёт – the lesson is in progress.
строительство идёт быстро – construction is going fast.
продвижение идёт медленно – progress is going slowly.

So идёт here means is proceeding / is going rather than physical walking.

Could the word order be моё продвижение медленно идёт instead of идёт медленно?

You can say:

моё продвижение медленно идёт

and it is grammatically correct, but it sounds a bit less natural in this particular context.

The neutral, most common order is:

моё продвижение идёт медленно

Putting медленно before идёт tends to add emphasis to медленно, almost contrasting it more:

Моё продвижение медленно идёт, но… – My progress is slowly going, but…

It’s not wrong; it just slightly shifts the rhythm and focus. The original version is the most typical word order for such a statement.

What does достаточно успешно mean exactly? Is достаточно “enough” or “quite”?

Достаточно can mean both:

enough / sufficiently
quite / rather / fairly

Here, with an adverb успешно (successfully), it’s closer to quite / fairly successfully:

идёт медленно, но достаточно успешно
→ is going slowly but quite successfully / but fairly successfully.

If the meaning were more like “successful enough” to meet some requirement, context would normally make that explicit, or you’d see достаточно used with a noun or adjective:

достаточно успехов – enough successes
достаточно успешный – sufficiently successful

In this sentence, native speakers usually hear it as rather / fairly successful.

Why is успешно an adverb and not an adjective like успешное продвижение?

The sentence describes how the process is going, not what kind of thing it is:

идёт как? – успешно (adverb, modifying the verb идёт).

If you said:

моё продвижение достаточно успешное

you would be using успешное as an adjective describing the noun продвижение:
my progress is quite successful (as a thing).

Both ways are correct, but:

идёт медленно, но достаточно успешно focuses on the manner of the process.
достаточно успешное продвижение would sound more like a static evaluation of your progress as an object.

What is the function of что here? Can you omit it like English sometimes omits that?

Here что is a conjunction meaning that, introducing a subordinate clause:

видеть, что моё продвижение идёт медленно…
→ to see that my progress is going slowly…

In English, you can often drop that:

I see (that) my progress is slow.

In Russian, you cannot usually omit что in this structure.
Without что, the sentence would sound ungrammatical or at best very strange:

✗ …помогают мне видеть моё продвижение идёт медленно… – wrong.

Russian needs the explicit conjunction что to mark the boundary between:

what you see (видеть), and
the clause that explains what you see.

Why are there commas both before что and before но?

Two different comma rules are at work:

Comma before что
Russian normally puts a comma before conjunctions that introduce subordinate clauses, like что, когда, потому что:
- …помогают мне видеть, что моё продвижение идёт медленно…
Here, что моё продвижение идёт медленно, но достаточно успешно is the entire subordinate clause after видеть.
Comma before но
Но is a coordinating conjunction meaning but. In Russian, you usually put a comma before coordinating conjunctions like и, а, но when they join two parts of a clause that both have their own predicate or are clearly contrastive:
- идёт медленно, но достаточно успешно

So each comma has its own standard justification in Russian punctuation rules.

Could заметки here mean “comments” or “memos,” or is it only “notes”?

Заметки is a fairly general word meaning notes / jottings / brief written remarks. Depending on context, it can be translated as:

notes (in a notebook, in an app)
jottings
brief remarks
sometimes comments, if you mean short written observations

Common nuances:

заметки в тетради – notes in a notebook.
делать заметки – to take notes.
короткие заметки в журнале – short pieces (little articles) in a magazine.

For official memos, Russian more often uses words like служебная записка, меморандум, not заметки.

In this sentence, эти заметки most naturally means these notes (e.g., study notes, progress notes).