Nah, there was no Communist insurgency inside Korea during Japanese rule. There were bandits running around but no major rebellions against Japanese rule in the peninsula.

In the borderlands between Korea, Manchuria, and Soviet Russia there were insurgents (Communist and otherwise). But even these guys were defeated and kicked out after Japan took over Manchuria in 1931.

The Japanese army really hated Communists...

I would place the blame squarely on the Soviet Union for turning North Korea Communist after 1945.

Korean nationalists want to talk romantically about the heroic efforts to fight for independence (and I understand this emotion) but the reality is that independence movements pretty much fizzled out. For example, the guy who drafted the March 1st, 1919 Declaration of Independence actively encouraged Koreans to work for the Japanese empire by 1943. [edit: I wonder why the Japanese colonial authorities didn't execute him. I can't imagine the British would have let go of Thomas Jefferson if they got a hold of him in 1776.]

Kyung Moon Hwang in A History of Korea discusses this in p190-195. I found this book to be a very readable book.

This is a somewhat complex question.

First off, /u/Nelson_Mac has the right of it, communism in Korea didn't start as a grass roots movement. Korea was divided because the US wanted a bufferzone between the USSR and Japan, and figured that giving the northern half of Korea would be a fair deal to the USSR. The Soviet Union, by contrast, wasn't expecting to get any of Korea, so they immediately agreed to take the norther portion of Korea. There were small communist factions working in Korea (as Yom Sang-seop's novel Three Generations talks about), and in fact Kim Il Sung was expecting the communist (or at least the anti-Rhee Syngnam) faction would quickly join his cause if he invaded the south (which was part of the reason why the Korean War started).

Both Kim Il-Sung and Rhee Syngnam were very much anti-imperialist and anti-Japanese, however Rhee was installed as the leader of South Korea by the US, and his power was contingent on positive relations with the US. This meant that whatever the US wanted to do, Rhee agreed to so that he could maintain his power, which meant allowing some of the former Japanese officials who had went around being jerks in Japanese occupied Korea to go back to being jerks in post-colonial Korea (they were already experienced and familiar with administrating over Korea, and the US was indifferent/ignorant as to how the Koreans would feel about this, so they put the former Japanese officials back into service). This also meant that if the US was anti-communist, so was Rhee, setting the precedent for the next two dictators to be heavily anti-communist as well.

Kim had the luxury of being anti-Japanese because his Soviet buddies didn't really care about who was administrating North Korea, as long as they were friendly to the USSR. This led Kim to make sure that none of the former Japanese administrators kept their jobs, and put a pretty nasty blackeye on Rhee in comparison. Like Rhee, Kim had to maintain a positive relationship with his allies, and quickly established many Soviet policies, including taking their cue and assuming cultural control in the literary and performance spheres.

Kim was the young, passionate, patriotic, war-hero who fought for Korean independence. Rhee was the politician from a prestigious family, received a western education, and spoke English, who wanted Korea to govern themselves again. Both had to kinda play lip service to their respective allies, and both wanted a Korea for Koreans, but outside politics got involved, and things got messy.

Hope this answers your question.