The Red Army was until the death of Stalin a political organ in all but name. Even after the end of the Dual Command structure every officer had his own political officer, and tens of thousands of other party officials were involved in everything from agitation to reducing desertion to ensuring party loyalty. All actions occurred with a degree of party oversight, and all officers were directly reported on by the NKVD. Beyond the public political system SMERSH, the NKVD, etc maintained a vast system of agents and informants. Communications, from telephones to letters, were observed constantly. By personal order of Stalin, Zhukov and other STAVKA officers were kept under close observation at all times, as were those close to them. Stalin began tightening the noose around Zhukov in particular before the war even ended, arresting officers that had previously been friends or affiliated with Zhukov to eliminate a potential power base and terrify him into submission.
Simply put, a coup was impossible.
To be honest the common soldier LOVED the man because the man knew how to fight and look after his troops, sure the man spent there lives like it was money but if he could help it he would not send them against a target if they could not take it.
Actually the opposite was true; Zhukov showed as much of a willingness to sacrifice tens of thousands of soldiers to achieve victory, though he recognized the difference between losses due to incompetence and losses due to the difficulty of their assigned objectives Commanders such as Vasilevsky, Rokossovsky, and Vatutin were less willing to accept such sacrifices. Part of that was due to Zhukov's hard-driving nature; he pushed himself and his subordinates to the limit in order to achieve objectives.
Very true which he should not of done he weakened the army so much the Americans could of walked over them if Pattons plan was accepted.
Not really; there was no public support for a long war, and a large amount of dissent even in the Anglo-American military. Any campaign against the Red Army would have lasted at least a year, and would be bloodier than any previous Anglo-American campaign; the political will for a new bloody war didn't exist in 1945 (Except if the Soviet Union attacked first).