In-text citation: what is the correct way of using both last name (i.e., \citeauthor ) and typical citation (i.e., \cite)
I don't think there is something like a general convention for this, aside from the usual rule of being consistent. So follow your personal/conference/journal/university/whatever style.

If that style dictates to use numbered references such as [1], always include this. Even if, like in your example, you start one of your sentences with the author name (and year). Note that (as @Ian_Fin mentions in the comments) the year is usually omitted when using an author name with number styled references.