Feeling unprepared for PhD because of poor educational system in my home country. Should I leave PhD to retake courses somewhere else?

In the European programs I have been involved in, there is no (or a very minimal) fixed curriculum students need to go through. However, students do follow specific courses to learn specific techniques. Typically/ideally the student discusses with her/his advisor what is needed for the project, what is needed for her/his future career, and where the gaps in her/his knowledge is, and how to fill those gaps. This is the kind of discussion you need to have with your advisor.

The university's name is not nearly important as your contributions. If you believe you have the talent required for a top university, but you say you don't have the education, then get the education.

Doing research requires you to be able to self-educate and then use that knowledge to push the boundaries and discover new solutions -- whether it is by inventing the method yourself or applying other people's methods to these problems.

This whole case sounds like you need to step back and evaluate yourself honestly. Then, buckle down and learn the things you think you need to know. You've already done the hard part of getting accepted, now do the harder part of making a plan and sticking to it. Talk to your adviser, figure out what you need to know, make a plan to learn it, and make sure you keep your eye on your research goals while doing so.

I'm not from mathematics, but your progress sounds reasonable to me. Midway to a paper after the first year is pretty good. That you missed closely related work is unfortunate, but not unusual: it's more or less the first time you are doing a real literature search. Ideally, your advisor should have checked that too.

I would caution against thinking that just because classwork is mandatory in other places, it will be good or useful. The classes offered at postgraduate level can vary wildly, and are often a motley collection of the research topics of the professors who get assigned to teach one. In my department, most of the postgraduate courses are too far from my work to be of practical use, and the one class I think I really could benefit from is taught by a professor that everyone has warned me to stay far away from.

The classes don't have to be mandatory for you to attend them. Especially when it is for your own learning, rather than for a grade, it is quite easy to just sit in on classes that you think you could benefit from. At the beginning of the semester, look through the classes offered at your local university and attend the first lecture of any that interest you. If it seems useful, talk to the professor at the end and ask if you can sit in informally. Usually there will be no problem, although if the exercises are only accessible through an online platform requiring students to be registered, like moodle, you may need to ask for access or for the prof to email you the materials separately (or you just find your own, different exercises).

This way, you can find out if extra classes would really be of as much value to you as you think they would be, without going to the drastic step of abandoning your PhD first.