You appear to have hidden the whole header, not just the header image, so of course you have no menu.
Check the setting both in Main Options > Header, and/or in the page editing page options.
And if you put your header image in the sitewide top area, of course it is smaller as that are is at the top of the content, but beside the sidebar.
You need to select hide header image not entire header. As for the area to put your other header image in, have a look at the insertion area page of the demo site to choose the one you want.
The preheader would be a good one. In the page editing page create a new custom field with that name, and put your content in it.
Do make sure that page is not a wordpress default blog page by going in Settings > Reading, set the front page to static, and have NOTHING selected in the post page drop down list (showing –select–)