All of the examples provided are valid HTML5, and all HTML5-compliant user agents are required to implement the HTML5 parsing algorithm, which constructs a DOM tree in a deterministic manner for any given input.
HTML5 specifically permits tag omission in many cases [1], including but not limited to both the opening and closing <html>, <head>, and <body> tags. The parsing algorithm provided in the standard generates a DOM tree that includes the omitted tags in the correct place(s).
For example, the following document is valid HTML5:
<!DOCTYPE html>
<title>Hello</title>
<p>Welcome to this example.