Occupying Eastern Europe was very much Stalin's idea, not Trotsky's. So was his support to Mao Zedong during the Communist Revolution in China, as well as the support to North Korea in the Korean war. After WWII, the Soviets decided that they needed a buffer against the West, and so claimed everything that they had liberated from the Nazis, except maybe Austria, and occupied Eastern Europe and North Korea.
Communism was thought to be a threat b'cos of the idea that Communist countries would fall in the Soviet sphere of influence, and make more easier their attempts to make governments all over the world Communist, and swearing allegiance to them. It wasn't the fear that you'd have Russian troops in Birmingham or Boston or Fairbanks. It would also have meant things like the abolition of the US constitution and entire government set up, and making the Communist Party of the US the replacement of Congress.
The complaints about Poland having a missile defense was made b'cos there was no recognition of the changed geopolitical realities since the end of the Cold War. For the 8 years after they collapsed, Russia had pretty much disappeared from the world map as a major influential power, and was pretty busy subduing the Chechen rebels and trying to resurrect their economy. The new enemy was Islam, which the West to this day refuses to recognize, much less acknowledge. There are still NATO troops in Iceland, Germany and Japan. But the threats to the West are more from resurgent Islamic countries - not just Iran, but potentially other Islamic countries as well via Jihad terrorism - countries like Pakistan, Afghanistan, Libya, Turkey, Yemen, Qatar, Saudi Arabia... Even if their governments may be superficially pro-US, their populations definitely ain't, and are very committed to supporting Jihadi campaigns against the West. Some may do it out of religious fervor, and others may do it just out of a good ole Third World envy and hatred of the West.