Google AdWords CPC traffic reported as "direct/none"

We have noticed that GA reports GAW-purchased clicks as direct traffic. Help pages describe this problem, but it doesn't solve our problem as we already have accounts linked and auto-tagging is on.
There's also no redirects used. So it's a mystery for now, why AdWords traffic is reported incorrectly.

Many versions of tracking code

When I tried to use Website Optimizer, I found that it doesn't use already installed Google Analytics tracking code. It needs another one.
Now I've found that if you want to use Conversion Tracking in AdWords, you need to install a separate code too.
Help page says in a "Advanced tracking options" section:
The Google Analytics Tracking Code will not interfere with the AdWords Conversion Tracking code if you use them at the same time on your site.
But do I get additional value from Conversion Tracking if I already use Google Analytics? This is still unclear to me.

Ad Variations need to collect enough statistics

I made several variation for an ad I use for my most effective ad group in AdWords. Now I've found that I accidentally made a duplicate. At 23k expressions one copy has CTR 0.69% and another one – 0.56%.

So the 0.13% CTR difference is statistically irrelevant at 23k expressions. This is unexpected. How much expressions should be there before one can make conclusions about ad variation effectiveness?

PS The difference is 0.06% now at 40k expressions for each of the copies.

I want to be an Analytics Pro

I decided to make some changes in my life and career, so I'm going to get all possible experience with Google Analytics and adjacent tools. My middle-term goal is to make an agency where I work an authorized Google analytics consultant. We have all needed resources - developers, clients etc, so I just need to get this moving.
I'm going to use this blog to make journal of my problems and discoveries.
I also need a writing practice in English, so I'll try my best not to make many mistakes, and I'll be glad to get corrections from the readers.