Are all of the red letter text the words of Jesus? To what extent can we be sure that the red letters in a KJV Bible are the actual words of Jesus?
The 'red letters' are not themselves part of the KJV translation. The red letters appear in many different translation of the Bible.

To answer the question: no, there is not universal agreement about exactly what words in the Bible were spoken by Jesus. The New Testament languages did not include punctuation like quote marks. Most of the time it is pretty clear from the text where Jesus words begin and end. Occasionally however it is hard to tell where a quote of Jesus ends and where an explanation from the Gospel author begins. For example in John 3 there is some uncertainty about whether Jesus quote which begins in verse 10 continues to verse 21 or stops after verse 15, with the remainder being explanation by the author.

If you are asking about actual words, then Jesus probably spoke in Aramaic, and so even the original Greek is not an untranslated quote. English and other modern language renditions are further translations.