Can someone give me a thorough explanation on なって?

Question

I get it that なって is a conjugation of なる (to become)

However, there are some thing I don't get, for example:

1 真赤になって怒っている.

He is red with anger.

なっている is the present progressive. However if you put a verb or anything of the sort between なって and いる will it still have the same meaning or is the meaning different ?

2 今週になって急速に株価が波乱含みになってきた.

Share prices are getting confused rapidly this week.

A conjugation of なって by itself without anything following it like (いる/でしょう etc.) doesn't exist from what I know. In that case what does it mean here? (The first one)

Also the きた which is after the なって (2nd) is also not a conjugation (from what I know)
So how does that work?

Answer 1

If the question 1 is asking if "なって" is "become", then it is yes. It consists of two parts.

1. (顔が) 真赤になっている
   The face has turned red and it is now (because of anger). The state of the face.
2. 怒っている
   Being furious. The state of the mind.

For question 2, "今週になって寒くなった" can be simpler to illustrate.

1. 今週になった
   The previous week has passed and a new week has began. Having turned into a new phase, also contrasting this week with before.
2. 寒くなった
   It has got cold. The state of climate condition has changed.

Meaning, it was not so cold last week, however after the new week has started, the weather changed and it is cold now.

Other examples.

• シーズン２になって、話がつまらなくなった
  With the season turned into the second, the story has got uninteresting.

I would suggest looking for a clue of change in state or phase. Such as:

He graduated high school and became a university student, and his attitude has changed drastically => 大学生になって、態度が変わった。

After the company has had a new CEO, the performance has slowed down => 新社長になって、業績が低迷した。