As an ordinary person, am I required to appoint one rabbi for myself, or at least several rabbis from our own generation, regarding the Jewish law I follow, because I do not consider myself competent to decide?

I am asking this because from what I understood in the article, if I am not competent to decide, then I cannot choose one approach when there is a dispute among halakhic decisors from earlier generations, and maybe even from our own generation.

You do indeed need to find a way to determine the Jewish law for yourself. A rabbi is an obvious solution.
When there is a dispute, you can follow one of the disputing opinions. Just not the leniencies of this one and that one.

Sorry, I do not understand the answer. The Talmud is the binding authority on the entire Jewish people. The Talmud was interpreted by rabbis throughout the generations, each with his own interpretation. I believe there is not a single thing about which there are no differing opinions—that is, dispute.

Can I, as an ordinary person, study each topic separately and, according to my own reasoning—not because it is more convenient—choose the halakhic decisor who interpreted the topic most correctly in my view, regardless of which generation he is from?

What is unclear? I wrote that I think there is no problem with this, since in the end you are acting in a way that a clear, authoritative halakhic decisor holds to be correct. There was no error here in an explicit Mishnah. In principle, you could even cast lots, except that there is a rule that in a case of doubt one should go stringently. I think that if you have a position, you may regard it as not being a state of doubt and not go stringently, even if you are not competent to decide. There is room for the claim that if you are not competent to decide, then you should treat it as a doubt, but in my opinion that is not necessary. Again, so long as you have not adopted the leniencies of this one and that one.

Why should the rule of doubt-stringency apply to me, as a person who always relies on some halakhic decisor from across the generations, seeing that the halakhic decisors throughout the generations already ruled according to that rule, did they not?

And in general, did you mean the rule that a Torah-level doubt is treated stringently and a rabbinic-level doubt leniently, or some other rule? Because I am having trouble understanding why it would be a Torah-level doubt to choose among a dispute between halakhic decisors.

Could you point me to some early source that would support the idea that I, as an ordinary person, can choose a side in different disputes among halakhic decisors after the Talmud?

Regarding "the leniencies of this one and that one," is it possible to say that the prohibition stated here applies to choosing the more convenient view when it does not sound logical to me, meaning I chose it only because it is convenient; whereas if there are many views that genuinely seem to me to be the correct ones, and it turns out that all of them are in fact more lenient, then this would no longer be the prohibition? I would be glad for an early source if you can, please.

I do not understand the question. You are in doubt between the opinions of the halakhic decisors, so the laws of doubt are applied. What is there to explain here?
I have no early source, and I do not know what an "early source" even means in this context or why such a thing is needed. This is a matter of reasoning.
If you chose something on its merits, there is no problem if it turns out leniently. The heart knows whether it is for integrity or for crookedness.

Because in the article you wrote that where there is doubt between opinions only someone competent to decide can decide, and here you answered me that not only such a person but also an ordinary person can.

Because I am an ordinary person, for every line of reasoning I have I look for some source among the halakhic decisors, and I always prefer earlier sources from the Geonim or medieval authorities. That is what I meant by "early source."

And one more thing that I may want to clarify: it could be that all the laws stated in the Talmud regarding doubts, "make for yourself a rabbi," "the leniencies of this one and that one," and so on, were all said with respect to learning from the Talmud itself, and they no longer apply afterward when deciding Jewish law among different commentators, who themselves already used those rules in order to interpret the Talmud into practical Jewish law.

I do not remember what I wrote there. Someone competent to decide can decide in an ordinary doubt. But when there is a doubt among great authorities, there is definitely room for the claim that anyone can decide, because in any case he has authorities on whom to rely.
I do not see a difference. They did not use these rules any more than the sages of the Talmud themselves did.