The "Add Text Comment" tool (formally know as the "Typewriter" tool) puts the entered characters on the PDF page as page content rather than in an annotation.
So, unlike Annotations which have, in the Annotation's Properties, a "Locked" choice for appearance the Add Text Comment does not.
In short there is no "locked" choice available for content placed via the Add Text Comment tool.
Use the "Add Text Box" tool instead, under Comments - Drawing Markups.
Can I remove that red box around the textbox ? Also, Can I put subscripts/superscripts and/or change fonts etc..etc..
Just to be clear, the Add Text Comment tool does create an annotation called a FreeText annotation, which you can see in the Content navigation pane. However, as Dave mentions, you cannot "lock" the annotation property.
If you use the Add Text Box command instead you can set the border to "No Border". Also, if you use the keyboard shortcut command Ctrl + e, you can also set the font and subscript/superscript properties.