The parsing of html syntax along with markdown is documented in GitHub Flavored Markdown Spec. Basically html along with nested markdown is not possible. However you can use html inside headings like # heading <input type="checkbox">.
Usually when using Obsidian you are not expected to specify any note‑specific formatting while writing content. By far more common is to specify global styling for every note using Themes or CSS snippets. However Obsidian allows individual note styling using cssclasses property. Usually cssclasses property is used in templates where CSS‑code has been written specially for that template. Writing CSS for individual notes is extremely clunky and unrecommended. In general if individual note styling is desired then Obsidian isn’t right choice for that purpose. Individual note styling can include inline formatting such as font, underline, subscript, superscript and text color—specifying these in the writing process in Obsidian is possible but extremely unrecommended since other free software is available for that exact purpose.
In some cases Obsidian users may want to use some restricted and fixed set of inline formatting syntax available using html. Usually such syntax is verbose but at least underline <u>text</u> and comments <!--text--> have simple syntax. Community plugins can be used to add extended inline formatting to Obsidian. However when content from Obsidian is desired to be shared as pdf files then using MS Word or Google Docs is highly recommended. In general there are no obvious ways to convert markdown to docx and complex software such as Pandoc must be used to convert markdown to docx which can then be opened in MS Word or Google Docs—related feature request: Copy-and-paste rendered version (no markdown) from the editor.