Yes there were a lot of KMT soldiers in PRC's armies. They switched sides to Communist during the Chinese Civil War as the Nationalist armies were retreating to Taiwan. Once, the Chinese Civil War was over, the Korean War was beginning to unfold. The troops didn't have time to go home, they had to be prepared for a war in Korea one more time.
The political leaders really wanted to invade Taiwan but with the Korean War, they changed their military plan and lost the opportunity to invade Taiwan.
No, it wasn't true that it was a way to get rid off potentially disloyal troops. They happened to be closer to Korea and didn't have time to go home for relaxation. Putting troops in Korea was mainly the decision of political leaders and military leaders. A number of Chinese civilians (perhaps University students as I had seen a photo) joined the troops. The belief from a Taiwanese was just an assumption. The claims of getting rid off disloyal troops were true earlier in the Chinese Civil war, but not in the Korean War, where PRC already consolidated armies. In the Chinese Civil War, both Communists and Nationalists were getting rid off/ laid off disloyal troops (mostly newly acquired prisoners) as part of their joint uneasy peace deal and in some early occasions killed troops perceived to be disloyal. So getting rid off disloyal troops was done already before the Korean War began.
When you have a small army early in a war, the usual way is to take no prisoners as you cannot afford to keep prisoners for too long. When your army get larger, you have two choices - kill prisoners or keep prisoners. It depends on your strategy.