Would it have been possible at some point during the 30's, for a lone soldier to assassinate Stalin and several his closet associates? What would have been the consequences and who could have taken charge?
I'm imagining a high ranking soldier of one of an ethnicity that Stalin didn't like. Maybe the soldier saw his family get wiped out by Stalin, and during one the purges he knows he'll be targeted for one reason or another. It could even be a small group of soldiers.
Interesting question. Up until the suicide of his wife, Stalin's personal security was fairly nominal. He used to walk around Moscow with Molotov and a single bodyguard. State Security provided his bodyguards, such as they were (many were purged as drunken incompetents). The Red Army was actually responsible for the external security of the Kremlin until 1936, so it's not impossible soldiers could get access to the Party leadership cadre prior to the mid-1930's.
After Stalin's wife died, there was massive upgrades in Kremlin security, with military elements being phased out in favor of State Security troops. After Stalin decided to purge the Red Army leadership, his personal security details grew exponentially, until they amounted to a private army numbering in the thousands. Generals meeting with Stalin were forbidden to carry firearms and routinely searched. Ordinary soldiers were also forbidden to be armed in Stalin's presence. As I recall it caused a stink at the Victory Parade in 1945-some Red Army officers took this security requirement as a personal insult.