2) The (optional) slider is designed to highlight some important posts (up to six). To make a post show in the slider, you mark it as a sticky and you set a suitably sized featured image to it.
When you create or edit a post, the sticky option is found in the Publish module of the post editor if you click "Edit" next to "Publish". To turn a post into a sticky after you have published it, you go to Posts > All Posts, hover over the post title, click Quick Edit, check the option "Make this post sticky", click Update.

3) The "recent articles" section automatically displays your latest three non-sticky posts; these posts also need to have a featured image. The "more articles" section automatically displays a further group of recent posts; the number of posts it displays is set in Settings > Reading. Naturally, if you haven't published enough posts, these sections will be empty or under-populated.

You cannot make a Page sticky. There is no option to do that as you have discovered. You can only find that option on a Post, not on a Page.

Public
_Stick this post to the front page
Password protected
Private

OK Cancel

Visibility: Public Edit
Public
Password protected
Password:
Private

OK Cancel

Nothing about sticky!

Visibility:
Public
Stick this post to the front page
Password protected
Private

OK Cancel

In Oxygen you can either have a Home page that displays your posts or a static front page ie. a Showcase template. http://en.support.wordpress.com/pages/front-page/#setting-up-a-static-front-page

Showcase page template
When you first activate Oxygen, you’ll see your posts in a traditional blog format but if you’d like to showcase your content in an online magazine-like fashion, then you can use the Showcase Page template. ...

Post thumbnails are 470 pixels wide, unless you make the post Sticky to show off in the featured slider, in which case they’re 750 pixels wide. Keep in mind: if you mark a post as Sticky but the featured image is less than 750 pixels wide, then it won’t display in the slider and will still disappear from the river of posts.
Please be aware that you cannot crop the sticky post thumbnails.

Sticky post thumbnails are 750 pixels wide in the featured slider
Regular post thumbnails are 470 pixels wide
http://en.support.wordpress.com/posts/post-visibility/#sticky-posts
Oxygen
http://en.support.wordpress.com/featured-images/#setting-a-featured-image

If you don't see the page attributes module then make sure that you don't have it hidden in your screen options http://en.support.wordpress.com/screen-options/
Modules to unhide:
Post – Likes and Shares, Format*, Categories, Tags, Excerpt, Send Trackbacks, Discussion, Comments**, Slug, Author, Revisions, Writing Helper
Page – Likes and Shares, Page Attributes, Featured Image, Discussion, Comments**, Page Revisions, Slug, Author, Revisions, Writing Helper

love the oxygen theme....it's doing wonders for my blogsite but seriously, their coders need to simplify the process.

my next complaint is how they took away a helluva bunch of options on their visual editor. (sigh)

btw love your site! keep it comin!

I went to my dashboard then went to Appearance --> Menus. I believe you have to create a new menu for the black background to pop up, so I created the categories menu and saved it. If you scroll down to the bottom of the menu page, there is a box on the left side that says "Theme Locations." I made my new menu (categories in my case!) the secondary menu. Then it just popped up!

Since I also had a widget that was categories, i went into Appearance --> Widgets, and deleted my categories widget. I hope that helps!