first experiences re compile and search

Just checking out Scrivener. I “get” the program and think it is a good choice for upcoming books. The first thing I tried (right out the box) was a compile to see what it looked like. I exported as Word. The resulting file, opened into Word, did not show heading styles, the headings were only bold with the whole file in a courier font which looks very weird. The sections and sub sections were not shown as headings, but all sections were simply listed one after the other, bold.
Why don’t these show up in a heirarchy?
Do I have to go through the whole Word document and format all of the heading sections there? Sounds brutal.
Then if I edit and want to get it back into Word, the whole thing again? hmm… I know I’m new to Scrivener, but please tell me I’m missing something re headings.

#2 - I don’t seem to be able to search the entire document, only the selected file. If I knew it was there, I wouldn’t be looking for it. Again, am I missing something?