how to create a link to mysite/user and how to theme mysite/user?
Like Stan Ascher posted the simplest and quickest way would probably be to create a block with the links and set it to appear where you want on the front page. With a wysiwyg editor it should be fairly easy to get the output themed to your liking as well.

If adding a block is not suitable for one reason or another there's also the option to manually add the necessary code in your theme's page--front.tpl.php file or if it doesn't exist then page.tpl.php. The code could look like this:

&lt;?php if ($is_front): ?&gt;
&lt;div class="user_links"&gt;
  &lt;?php print l(t('login'), 'user', array('attributes' =&gt; array('class' =&gt; array('login')))); ?&gt;
  &lt;span&gt; | &lt;/span&gt;
  &lt;?php print l(t('register'), 'user/register', array('attributes' =&gt; array('class' =&gt; array('register')))); ?&gt;
&lt;/div&gt;
&lt;?php endif; ?&gt;


If the code is going into page--front.tpl.php then remove the first and last line. Basic HTML, CSS knowledge would probably be necessary with this approach though.

You can add fields for users on the 'admin/config/people/accounts/fields' page or select Configuration -> Account settings then the manage fields tab. These can be set to appear on user registration and users can edit them later with their other profile information.