I struggle a lot with syntax and articles in the language I'm learning, too. I think they are probably the most challenging aspects of learning any new language. It can be hard to remember all the rules, so perhaps just memorization isn't the best way to go. Have you tried reading books in English? Gaining familiarity with syntax through repeated exposure to written forms of entertainment might help. You write well, so I presume that you can read fairly fluently. That should mean that you'd be able to absorb typical usage subconsciously while you read. Perhaps you could read a novel with a plot that interests you, or a non-fiction book on a topic you're interested in? If you don't know where to start, you could check out Goodreads.com for recommendations; on each book's page, they have a "readers also enjoyed" section, so you can search for a book you already like and find something similar.

I've marked less natural phrasings with orange, more natural phrasings with purple, and corrections with green.

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I still can't cope with English syntax. Most of corrections I get are related to a non-English way to connect words and express things. Words are mostly right but their relationships are wrong. I don't know how to fix it; probably it's a matter of time and slow memorizing\memorization. [1] One has to think in English to make it right. I mostly can't do that. / For the most part, I can't do that. [2]

One more problem is articles. I'm in despair [3] when I see that I'm still far from clearly understanding [4] how to use them. I know several general rules and try to use them intuitively, but make mistakes much more frequently than I correctly guess what to choose use. [5]

Another problem is phrasal verbs, although I would say I master them step by step. This task is quite clear: nothing can help other than\besides memorization and practicing. [6]

So, as you see I know "who my enemies are", and this is the only fact that makes me optimistic.

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1. Both words are grammatically correct here, but "memorization" is the more natural one.

2. "Mostly" is grammatical, and some native English speakers would phrase the sentence the way you did, but I added another more common option.

3. This is correct, natural, and grammatical, but you could also phrase it with the verb form of "despair": "I despair when I see..."

4. You could phrase this as "I'm still far from clearly understanding how to use them" or "I'm still far from a clear understanding of how to use them." They're equally natural.

5. I added "correctly" because "guess" is neutral; you could make a correct guess or an incorrect guess, so this adds clarity. "Choose" makes sense, but it is a little redundant with "guess" (guessing is a form of choosing), so "use" is a better option here. Alternatively, you could say "than I guess the right choice."

6. Both "other than" and "besides" are correct and natural here. You can pick whichever you like better. "Practicing" is a gerund, and it is grammatically correct here, but since the noun "practice" exists, it'd be a slightly more natural choice to pair with the noun "memorization." "Memorizing and practicing" (both gerunds) would also be natural.

Keep up the good work!