If the original poster still needs help after nine months, then the exact code would be:
<?php if ( ! is_page( 'newsletter-sign-up' ) { ?>
<?php if (is_home()):?>
<h1><a href="<?php echo home_url( '' ); ?>/"><?php bloginfo('name'); ?></a></h1>
<?php else:?>
<h3><a href="<?php echo home_url( '' ); ?>/"><?php bloginfo('name'); ?></a></h3>
<?php endif;?>
<div class="description"><?php bloginfo('description'); ?></div>
<?php } ?>
The bit inside the conditional is already in “header.php”; I just added it to make clear what part to surround.
A slightly easier way would be to use the conditional already in place; replace this line:
<?php if ($options[$shortname . '_show_blog_title_and_description']=='yes'):?>
with:
<?php if ($options[$shortname . '_show_blog_title_and_description']=='yes' && ( ! is_page( 'newsletter-sign-up' ) ) ):?>
As for the new question, I don’t use the Weaver theme so I have no idea what its file structure is or how it goes about doing things and without seeing the generated code of your site I can’t infer how it works. The code your looking to alter is usually found in the theme’s “header.php” file. If you find the code used to display the title…
Probably looks something like this:
<h1><?php bloginfo('name'); ?></h1>
…then you can wrap it in a conditional that causes it to refrain from displaying on the “front” page:
<?php if ( ! is_front_page() ) { ?>
<h1><?php bloginfo('name'); ?></h1>
<?php } ?>
If your site’s styling goes wonky without having that <h1> tag (or whatever tag used in displaying the title) then you could do something like:
<?php if ( ! is_front_page() ) { ?>
<h1><?php bloginfo('name'); ?></h1>
<?php } else { ?>
<h1></h1>
<?php } ?>