Okay, and you’re sure you’re actually getting 800mb? If you are on a shared hosting it’s possible your own changes to for example wp-config or htaccess isn’t being used.
Could you try creating a file info.php in your server root and place:
<?php phpinfo(); ?> in it. Then go to yourdomain.com/info.php .. There you should be able to find what your memory_limit and max_input_vars are really set to.
As for the php errors it’s only the last one about headers that I think might be doing some actual damage. Seems something (either your theme or a plugin) is trying to output things before they should.
