Worthy of their Mettle: a Superhero Timeline

Yes. The US has steadily ramped up its occupational forces over those years, increasing after the end of most combat in Russia around 2000 and another surge in the late 2000s. 

The actual war in Guatemala has taken a good few thousand dead, not counting the millions dead in Vucub-Caquix's direct attack on the US in the 80s. 

There are definitely antiwar demonstrations; there was one at the memorial in Miami a few updates back. 

Excerpt from a BBC article, What You Need to Know About the Post-Soviet Peacekeeping Mission, 2010

As it currently stands the United Kingdom provides the majority of peacekeeping forces in the four Baltic states of Estonia, Latvia, Lithuania, and Konigsberg, and retains significant deployment in Poland, Belarus, Ukraine, and Russia. Germany is charged with keeping the peace in the former German Democratic Republic, Italy and France cover Czechoslovakia and Hungary, plus parts of Poland and Ukraine, and a coalition of Turkey (who also has deployments in the Caucasus), Greece, Spain, and Portugal oversee Romania, Bulgaria, and Albania.

The United States has highest authority over the forces in the former Eastern Bloc, and control the majority of forces within Russia proper. These forces are backed by those from Canada and other lesser contingents from other European states, as well as Japan, South Korea, the Philippines, and certain Latin American countries.

[...]

The entire mission has its field command in the main US base, Fort Seward, in Moscow, which has direct communication with the Kremlin (this was established under Boris Yeltsin and retained among other presidents including the current president Nemtsov). There are other Allied bases in major former Soviet cities and naval bases in the Arctic and on the Russian pacific coast.

British forces in particular run their occupational zone from Riga.

[...]

The occupation was deemed necessary by NATO high command when the coup against reformist leader Eduard Shevardnadze, led by the superhuman form of Vladimir Lenin and assisted by several other hardliner Soviet superhumans successfully breached the walls of the Kremlin and almost took Shevardnadze hostage; he escaped by loyalist superhuman aid. This plunged the entire Soviet Union into a civil war that mirrored those unfolding in the rest of Eastern Europe.

The other countries of the Soviet bloc had devolved into chaos with the rise of populist anticommunist movements which were violently cracked down on the behalf of particularly loyal superhumans in league with the security services. By 1989 all of them were in chaos to some degree, and by 1991 the Soviet Union had collapsed into murderous squabbling.

[...]

Superhuman activity caused the devastation of several cities, and the split between hardliners and loyalists went to the highest echelons of the Soviet military infrastructure. Soon, hardliners gained control of nuclear weapons, and seven were used in the conflict, each one obliterating large portions of a city; the largest was Omsk. Similar fighting between superhumans devastated still more cities, including the destruction of a good part of the Kremlin complex itself.

[...]

It was the use of nuclear weapons that convinced the Allies under the auspices of NATO to intervene with the purpose of containing rogue superhumans and nuclear weapons. One very explicit goal was the apprehension or destruction of Vladimir Lenin. Since this was interpreted as a threat to all NATO member states, Article V was invoked for all parties.

[...]

Despite the ultimate Allied victory, there are still flareups in the occupied Eastern Bloc. One of the most important causes is the continued presence of Vladimir Lenin causing havoc and then fleeing abroad. It is believed that he has some sort of hideaway in Antarctica, but this location in particular is unknown.

Konigsberg is Kaliningrad given back its old name and split off from Russia. Still mostly ethnic Russian.

Kosygin deliberately did not make Stalin immortal as to avoid another personality cult.  

Not worshiped no, but seen by many as the foremost vanguard of Communism. 

Not in a supernatural way no. A following, yes, but more like Che than Jesus.