Are <html> <head> and <body> necessary?

Would it be somehow wrong if I don’t use this tags in a HTML5 page?

https://html.spec.whatwg.org/multipage/syntax.html#syntax-tag-omission

In short, I can omit this tags as long I don’t care where my comments are?

Yes, but I would recommend you no to omit them - it’s easier for others to read your code.
Check out this tool called Emmet.