1. The location of the inline TOC created (if any) is up to program you are using to convert the book. If you are using calibre, I believe there's some setting for that. You'd be better saved asking this in the calibre forum, as this is only marginally related to ePub.
2. The titles in the text and in the TOC are totally independent, you can have whatever words you want in both (even in an inline TOC, if it exists). It is only if you are creating the TOC automatically with some tool that the titles are copied from the text. In that case, you should tell us which tool you are using. You can "hide" some words from the text wrapping them in a <span> (or whatever) with a "display: none" style. In Sigil (and maybe other programs) you can assign a different name for the TOC adding a "title" attribute, so these would be roughly equivalent:
Code:
<h3><span class="hidden">Chapter 1</span></h3>
/*with this in CSS:*/
span.hidden { display: none; }
Code:
<h3 title="Chapter 1"> </h3>
(The second may be better for conversion to Mobi, as Mobi does not support CSS, and the converter might not interpret "display: none" correctly.)