The Mueller report and Barrs summary leave so many un answered questions..Why did the Russians decided to back Trump over Hillary?..?

Clinton wasn't a good candidate from the Russian perspective. First off, anything which makes the US strong is bad for Russia, or at least bad for Putin who has made us his enemy. Clinton would have been a strong leader, particularly on the international front where she was well known and well regarded. But they also disliked her for her strong stand against Putin and his interests. Clinton had first earned his ire, IIRC when she criticized a rigged election which he won. She has been critical of Rusian violence abroad and had advocated for the US to intervene in Syria against the Russian ally Bashar al Assad. Clinton, as President, would have continued, and even strengthened, the Obama era policy of trying to contain Russian adventurism through sanctions, diplomacy, and a stronger NATO.

Trump, OTOH, was an absolute dream. For whatever reason, Trump took Moscow's side on literally every issue. He criticized NATO, he justified the annexation of Crimea, he called for the US getting out of Syria, her personally praised Vladimir Putin, and he called for the end of US sanctions against Russia. Putin also knew that Trump would be a weak and divisive leader for the US, which was good for him. Putin knows Trump is an idiot. As a failed businessmen and reality tv host with no political experience he would be a weak and ineffective leader for the US. His isolation from the Republican party establishment would hamper his effectiveness. His total lack of foreign policy experience would be a tremendous boon for Russia. So would his racism and xenophobia which alienated many American allies and harmed America's image throughout the world. Trump's egomania would mean that he would be unable to accept constructive advice and learn from mistakes. His narcissism meant that he would be easily manipulated through flattery, and his corrupt nature would allow the possibility that Moscow could bribe him with business deals or straight out cash infusions.

The intent of Russians was to cause division in the political system of the U.S. A division that was swallowed hook line and sinker by the media, politicians, and their political followers.

Because they know that he's corrupt. Putin likes corrupt people.

Nothing remarkable, Putin/Russia assumed that a trump presidency was in Russia's long term interests

You are seeing why. The Russian didn't care who won. What they wanted to do is sow discord. The Russians knew very well that the media is run by leftists.

The Russians put their taint of obstruction on both Hillary with the Steele dossier and Trump with the released emails. They KNEW that if Hilary was elected, the leftist media would cover for Hillary and this would go into the long list of conservative conspiracy theories.

If Trump got elected, however, the leftist media would go NUTS and they did.

Now you see an extremely low level of trust in Congress, the presidency, the courts and the media. Every major US institution of power has been negatively impacted by this.

Hillary attempted to meddle in the Russian elections when she was SOS.

Trump has a long history with Russian oligarchs. I'm sure Putin has tons of dirt on him.

The Mueller Report is not intended to answer these kinds of questions.

The Russians and Hilary have never been friends.
Part of it dates back to Bill Clinton's Presidency but it took hold while Hilary was Secretary of State.
For example: in 2011 Putin blamed Hilary for rioting that was occurring.

I think the Russians played it both ways. Mueller "forgot" to mention that.

In fact, he forgot to mention quite a lot. The report reads more like an op ed against Trump than the results of a detailed investigation. He never investigated the supposedly hacked servers, for instance. Why not? He never questioned or attempted to question Julian Assange who would know some of the answers.

They did help Hillary. Heck, Hillary supporters in positions of power even accepted help from Russia, Trump's people did not.