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1. How do i see in G analytics, if people searched for keyword "x" on a specific organic search engine and who of them or how many registered the site or made a purchase and which purchase?
i want to be able to see the entire thing- organic search (which SE and what Key Word, led to which sale)
First you have to configure goals. This means naming the "goal" pages as G1 / G2 / G3 etc. You do this in the >Analytics Settings / Edit Mode and it is really quite simple. You just name your "target" page. For me I named the thank_you page. Others might be a view to a "contact us" page or a "dealers page". All you have to do is name the page. Of course all your pages must have the tracking code on them.
Then let it run for a few days so you get some good data.
Then go into GA, >View Reports, click on Marketing Optimization, Search Engine Marketing and Overall Keyword Conversion and you should be home free.
You could also do it without setting goals, it is a bit cruder, but you could look in Content Optimization and then Content Performance for your specific content, then use the purple button with the upward pointing double arrows, then scroll down to "keywords". This shows you what terms were used when visiting this page - but not by engine etc.
Both of these approaches are particularly powerful features that really lets you know what's going on.
Hope that helps!