Theming the userpage
Yes, THEMENAME_preprocess_page() is fine for this, but one could argue that it's better to implement hook_user when $op == 'view'. That way you would make the change available for all themes (who knows you will be adding a mobile theme a couple of months from now?).
I wouldn't use THEMENAME_menu_local_tasks() for this, but instead do $variables['tabs'] = ''; in THEMENAME_preprocess_page(). Of course, only do this for the user page, otherwise you will lose the tabs on all pages.
Yes, use user-profile.tpl.php to print out variables. If you need additional variables, fetch them in THEMENAME_preprocess_page() and add them to the $variables array to make them available in your template. Depending on what you need to do, see also user-profile-category.tpl.php, user-profile-item.tpl.php and their respective preprocess functions.
Yes, that's an option. You can also create a block display of that view and enable the block on the user page.


I recommend not to use multiple page templates (like page-user.tpl.php) if you can. When you do, a simple change to page.tpl.php will often need to be applied to all other page templates as well, which is a bore.