System 1 and unconsious Kahneman (2011) apparently suggests there is system 1 and system 2 in decision making.

If I am not wrong he says system 1 is more prone to errors because it is automatic. Is this correct assumption of mine?

If yes, next question I have is: Is system1 related to unconcious? If yes, then isn't there a conflict between above assumption and this one:

that unconscious thought (UT) is better at solving complex tasks,
where many variables are considered, than conscious thought.

So if UT is related to System 1, then doesn't it contradict Kahnemans view that System 1 is more prone to errors (because if it is prone to errors according to Kahneman how is it better at decision making according to Wiki)? Needless to say there are articles which don't agree with wiki article I linked. This one for example: Acker (2008).
References
Acker, F. (2008). New findings on unconscious versus conscious thought in decision making: Additional empirical data and meta-analysis. Judgment and Decision Making, 3(4), 292-303.
Kahneman, D. (2011). Thinking, Fast and Slow. New York: Farrar, Straus and Giroux
You are correct in System 1 being more prone to errors as it relies on emotional experiences in the moment along with stereotypes and frequency of event.
System 2

You wouldn’t expect someone to  quickly ( in a matter of seconds ) spit out the answer to the question “calculate the mass of this (random) object” if the person has never experienced this object before.

System 1

You would expect someone to apply the brake when they see a red light.

According to Kahneman (2011) System 1 is brought on by emotional experience and in the moment thought. This is a stronger and faster experience than that of which system 2 is capable of overriding. System 2 takes time to meditate a plan or course of action whereas system 1 is more of an immediate response. This delay in response would therefore suggest the latency between the workings of both systems.
This is of course my interpretation of his book “Thinking, Fast and Slow” and has room for subjective debate.
He does provide wonderful examples pertaining to stock brokers and their tendency to follow the hype of the crowd and sell when it is often best to ride it out. I do not have the book currently on hand but will comment the reference when i have it.
References
Kahneman, D. (2011). Thinking, Fast and Slow. New York: Farrar, Straus and Giroux