Adding up to the questions linked by Robotnique:

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Kutuzov's trying to hold back the armies to let the French flee withoutuseless battles, him being the only one "knowing" the war was won justafter Borodino etc

This is a complicated question and the one which was usually answered differently from different points of view throughout the history. Many Russian commanders and the emperor himself often expressed dissatisfaction with Kutuzov's actions.

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First, general Barclay later claimed that he deemed position at Zarevo-Zaimische, taken earlier by Russian army against Napoleon, to be much better suited for defensive action than Borodino (where the actual battle happened later), and was annoyed by the fact that Kutuzov outright refused to outlook the battlefield and ordered immediate relocation once again. It's much more likely that Kutuzov actually ordered further retreat to reinforce his army with additional detachments and Moscow militia, but still army and ruling elite took this action rather unfavourably.

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Second, Kutuzov seemingly wanted to actually halt Napoleon's advance at Borodino, but couldn't do so and had to retreat once again. He would later actively discourage his subordinates from attacking French army and hastily retreat instead of facing them in the open field - again, much to the infuriation of the emperor and Russian society. After he heard of Napoleon's forces turning back, he actually organized quick pursuit but once again stopped majority of his reserves from advancing forth at Krasnoi. Even when French came close to Berezina, Kutuzov lagged far behind, allowing two additional corps (under command of Chichagov and Wittgenstein) to finish the work (which they didn't: Napoleon escaped). This, once again, severely dropped Kutuzov's image in the eyes of the public.

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I'm personally of an opinion that Kutuzov was very cautious because he didn't want to risk defeat in the open field against Napoleon in the final stages of the campaign. There are several possible explanations about Kutuzov's actions from different points of view, including famous line about Napoleon's escape being profitable to Russia and that catching Napoleon now would needlessly strengthen Great Britain's positions, but we don't know if he actually said what he meant and if he meant it at all, because he wasn't a man of many words when explaining his motivation.

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I'd say that Tolstoy's depiction of Kutuzov's action is a bit too dramatic, exposing him as the all-knowing intelligent mastermind. In reality his actions were often contested by other officers, and it's usually perceived that he was indeed way too slow and uncertain in attacking retreating French forces.

Past answers: here by /u/SgtBANZAI

Napoleon's campaign discussed further here

For outside resources you might want to look into "Truth and lies in Leo Tolstoy's War and Peace" by Fraser Bell. Available through GALE OneFile here

The latter requires access through a subscription. I can't post the body of the text here, but PM me if you want to read it (mods: I'm not pirating, I have access as a librarian). Having quickly read over it, I think it does a good job of answering your questions about Borodino and Kutuzov.

That all being said, clearly there's a lot more to say if somebody steps up to the plate, but hopefully this will tide you over until then.

In Russia***