hide navigation and header on mobile

You can follow the instructions here to customize the look of Jetpack’s Mobile Theme:
http://jetpack.me/2013/06/27/customize-mobile-theme/

Thanks to the Custom CSS module, you’ll be able to add custom CSS to your mobile theme to hide the header. This CSS should do the trick:

.mobile-theme .menu-search {
	display: none;
}

1 how do i remove the auto-generated header with the site’s name? my theme has no header.
2. how do i remove the site’s title? on the page i can define to hide page title, but the mobile theme still displays it.

You can hide the header (including the site’s name) with the following CSS:

.mobile-theme #branding {
	display: none;
}

Beware, though: once you do so mobile readers won’t be able to find their way back to your home page once they’re looking at a single post or page.

3. i put a clickable phone number in the header.
on desktop you see it, it’s there. on mobile theme you don’t see it. it’s not there. how do i display it?

I’m not sure where you’d put it once you remove the menu bar, the search form, and the Site Title area. Maybe instead of the Site Title, like so?
http://i.wpne.ws/Zxr4

You can do so with the following CSS:

.mobile-theme #branding {
	display: block;
}
.mobile-theme .site-branding {
	display: none;
}
.mobile-theme #branding:before {
	content: '0102030405';
	color: #111;
	font-size: 1.846em;
	font-weight: bold;
	line-height: 1.3;
}

4. where can i find the mobile theme’s html of the page, so i can see names of div’s etc.
5. where can i find the css of the mobile theme?

You can use your browser inspector to find out more about the mobile theme structure as well as the CSS applied to each element.

If you use Chrome, you can follow these instructions:
https://developer.chrome.com/devtools/docs/device-mode
https://developer.chrome.com/devtools/docs/elements-styles

You can then paste all your custom CSS inside the custom CSS editor in your dashboard, under Appearance > Edit CSS.

as for the mobile’s page html, is it identical to the desktop’s version?

No, it’s a specific theme. Chrome’s dev tools will help you there, as it will allow you to see the structure when on a mobile device.

still can’t find a way to hide the page tile (the name of the page.

in my theme i selected to hide it, and still the name is displayed, it seems auto generated with the page’s name.
can’t get rid of it.

Could you post a screenshot of how things are displayed on your end, and let me know exactly what you’d like to remove? I’m not sure I understand what you’d like to remove.

@pa-plinka If your theme is already responsive, I’d suggest that you disable Jetpack’s Mobile Theme module under Jetpack > Settings in your dashboard.

@belovedarrow I had a look at your site, and you don’t seem to be using the Jetpack Mobile Theme right now. You’ll want to contact your theme author for help:
http://themeforest.net/item/avatar-one-multi-page-parallax-wordpress-theme/9450806