Hey,
1) You can remove the "Archive for..." text in archive.php - search fot following code and delete it:
<h2><?php /* If this is a category archive */ if (is_category()) { ?>
<?php _e('Archive for','newscast'); ?> <?php echo single_cat_title(); ?>
<?php /* If this is a daily archive */ } elseif (is_day()) { ?>
<?php _e('Archive for','newscast'); ?> <?php the_time('F jS, Y'); ?>
<?php /* If this is a monthly archive */ } elseif (is_month()) { ?>
<?php _e('Archive for','newscast'); ?> <?php the_time('F, Y'); ?>
<?php /* If this is a yearly archive */ } elseif (is_year()) { ?>
<?php _e('Archive for','newscast'); ?> <?php the_time('Y'); ?>
<?php /* If this is a search */ } elseif (is_search()) { ?>
<?php _e('Search Results','newscast'); ?>
<?php /* If this is an author archive */ } elseif (is_author()) { ?>
<?php _e('Author Archive','newscast'); ?>
<?php /* If this is a paged archive */ } elseif (isset($_GET['paged']) && !empty($_GET['paged'])) { ?>
<?php _e('Blog Archives','newscast'); ?>
<?php } ?></h2>
2) I'm not sure if I understood you right but it sounds like you want to remove the page titles. f yes open up page.php and template-fullwidth.php and delete:
<h1 class="entry-heading">
<a href="<?php echo get_permalink() ?>" rel="bookmark" title="<?php _e('Permanent Link:','newscast')?> <?php the_title(); ?>">
<?php the_title(); ?>
</a>
</h1>
3) You can create a custom menu (Appearance > Menus) - I'd just create a link, call it "home" and link it to the main url.