Code in nodes can shutdown entire drupal site

Sites usually break when broken code is loaded for all pages, like in modules, blocks, themes and templates.
But pages with broken php code only execute when that individual page loads.
If you "promoted" it to the frontpage then the frontpage will break as well as any list with teasers like taxonomy pages.

Try to see if there's any pages that do not break.
For example, try to edit the node directly, or see if you can get to the admin pages, where you can simply unpublish it.
Unless the code ran in the theme or you had a broken block those pages shouldn't break.

You have to check how exactly you loaded your static pages.
If you just pasted some code in a node it would only run if you selected "php code" in the filters.
You must also see what code it was, perhaps it had javascript on it, or html head tags.
But again, that would only break that particular pages.

Try to remember of other recent changes that could have caused site wide effects.
For example, was RPG.module properly uninstalled? Did you use a new theme? custom blocks?
If you can't get to the admin pages, you are stuck with a manual removal of the code on the sql tables.
Was your code in several nodes? Where exactly you removed it?
Dropping tables will also drop everything on it, which is no sensible solution.
Usually the best practices are to have a backup, and a test site.

After fixing it, you should also check your error logs. php and mysql errors are left on the server logs.
On a shared server the support techs should be able to give you hints about the offending function.
Those errors usually include the module name, block or theme, so you can easily identify the culprit.

You'll need to be more specific. Lots of sites use HTML in page bodies just fine, so there must be something specifically wrong with the HTML you put in the page or with your Drupal install. Can you try testing the HTML to see what makes it break? Does just a simple i or b tag break it, or does it have to be a full page with html and body tags (hint: don't do that anyway)? When you get a white page, check View Source to see if you're getting nothing (indicating the server died) or some garbled HTML that just happens to not render. What version of PHP/Apache/MySQL are you running?

There's no way to identify the bug if we aren't able to reproduce it specifically.

Using Full HTML means Drupal won't protect you against inputting HTML that is horribly invalid and will break the browser. Having a full page with /code> tag inside the body of the page is horribly invalid and will break the browser. :-) It sounds like a combination of user error (using horribly invalid HTML) and the browser not handling that edge case (although I don't blame it). If Drupal is generating the HTML one would expect in that case (a full HTML page inside the content area within the body tag), then it's not a Drupal bug and this should be marked won't fix.

OK. If it's caused by an import module you usually want to file a bug against that module rather than Drupal core itself.