Continuous action: 在、着、or 在。。着

The usage of 着 vs 在 has always confused me when it comes to making up my own sentences.  My impression is that 着 is often used as a background to another action:

 他拿着书信站起来。

or to just describe a "state"

他就在站着拿着刚来的书信。

What about：

他在写信。

It seems unnatural to say：他写着信。

What the difference between:

他看着我。

他在看我。

他在看着我。

Thanks!