I tested after #2 was resolved (🎉 thanks!) by entering the HTML snippet and no Base URL:

<div class="h-entry">
  <h1 class="p-name">Test Post</h1>
  <div class="e-content"><p>Lorem ipsum</p></div>
</div>

I got "Internal Server Error"

I tried again, entering the Base URL https://example.com and it worked.

It should probably support parsing without a base URL like the other parser sites, or at least require the Base URL field to avoid the error.