Have you checked the Kendo UI Mobile ThemeBuilder already? While you can't edit the NavBar height and border-radiuses, it may help you with some of the styling required.
That said, lets go over your questions:
1. All interface elements in Kendo UI Mobile are relative and depend on the font-size to allow easy resizing. You can change the font-size of the NavBar to resize it. NavBar height is also dependent by the View Title height. So, if you change the View Title line-height, it will resize the NavBar too. Choose the one that best suits your use case.
2. The border-radius of the list items is set on the first and last item only and has a rather high specificity. To change it, try like this:
.km-ios .km-listinset > li:first-child,
.km-ios .km-listgroupinset .km-list > li:first-child
-webkit-border-radius: 10px 10px 0 0;
border-radius: 10px 10px 0 0;
.km-ios .km-listinset > li:last-child,
.km-ios .km-listgroupinset .km-list > li:last-child
-webkit-border-radius: 0 0 10px 10px;
border-radius: 0 0 10px 10px;
.km-ios .km-listinset > li:first-child:last-child,
.km-ios .km-listgroupinset .km-list > li:first-child:last-child
3. Kendo UI Mobile doesn't offer anything specific about that, check this article
how to work with application cache.
4. Currently the loader uses a font icon for the spinner as there are issues with WebKit masks on some platforms. The image there is auto rotated. You can use a plain image like this:
The text is placed in an H1 element inside the loader, remove it like this:
.km-ios .km-loader h1
5. The styles above use the .km-ios class which will constrain them only to iOS, so - no. Replace it with .km-root to target all platforms (though better not do it for the loading image as on WP it is handled very differently).
6. Unfortunately I'm not aware of such project.
the Telerik team
Join us on our journey to create the world's most complete HTML 5 UI Framework - download Kendo UI