In Gettier's "Is Justified True Belief Knowledge?" he stated a form: S knows that P is true IFF: P is true S believes that P is true, and S is justified in believing that P is true. What does this form mean? Why did Gettier argue that this statement is false and that it doesn't constitute sufficient conditions for knowledge? In the second part of his journal, he employs an inductive rule. He cites that something that happens in the past has patterns, so something similar that happens in the future will probably encounter a similar result. What is he trying to approach by using this inductive rule?

This is tricky, as Gettier's ideas try to follow a tightrope of logic that is somewhat precarious. Let's break it down with examples along the way.
We'll use the characters he frequently employed, Smith and Jones. The goal is for Smith to know fact P based on the logical steps (IFF means if and only if, thereby including the steps below and excluding all other options or knowledge):

Fact P must be true, Smith must believe that fact P is true, and Smith must have some valid justification for believing in P.

For instance, take the counterexample that Gettier uses of Smith and Jones going for a job interview. Fact P is that Jones will get the job. There is additional information that Smith knows; he knows that Jones has 10 coins in his pocket, but he does not know that he has 10 coins in his own pocket. So, Smith believes that the man who has 10 coins in his pocket (in his mind this is Jones only) will get the job, and his justification for believing that is that he knows Jones will get the job and that Jones has 10 coins in his pocket.
However, there is a fallacy here: Fact P at the beginning is not the same as Fact P at the end, so we'll call it Fact Q. Fact P is that Jones will get the job, which we know. But the ending Fact is that the man with 10 coins in his pocket will get the job. This is separate, and the justification for this fact is based on incomplete knowledge. Thus, Gettier answers the question he puts forth: justified true belief is not (always) knowledge.
Later, he discusses the pattern of something in the past indicating the pattern of something in the future as a foundational belief for reason. However, he states that believing that past patterns can predict future patterns is a flawed method of logic. He argues that it will only lead to belief and supposition without any true revelation of knowledge. Thus, his argument is founded on the idea that there are always deviations in patterns; we won't know for certain if what we believe (based on historical events) will come to pass, no matter how much we believe in them and feel that belief is justified.