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Try with the following file:

#+STARTUP: overview

* Chores
:PROPERTIES:
:VISIBILITY: all
:END:
** NEXT Brush Teeth in Day
   SCHEDULED: <2020-10-22 Thu +1d>
** NEXT Brush & Floss Teeth at Night
   SCHEDULED: <2020-10-21 Wed +1d>
* Math
  math
* English
  english
* Geology
  geology

Save the file, close it and reopen it: I believe that will do what you want.

Note that:

• the PROPERTIES drawer must NOT be commented out (as it was in your example).
• VISIBILITY was spelled incorrectly.
• VISIBILITY values are: folded, children, content, and all - in particular, they are NOT the same as the values required in the #+STARTUP: keyword line. See Initial Visibility.
• the #+STARTUP: keyword setting is global for the file - it is good practice to put it at the top of the file. And note how it is spelled: the #+ prefix for keywords is essential.

EDIT: The manual has a lot of information, including what the #+STARTUP: values mean. Even though I provide a link to the appropriate section here, the best way to navigate the manual (not only the Org mode manual, but also the Emacs manual and eventually the Emacs Lisp manual and all the other manuals that come with Emacs and any other manuals in Info format that you might add), is to do it in Emacs itself. Say C-h i m Org M<TAB> RET and search the index for #+STARTUP (i startup RET). It says there are 23 places in the manual where that term occurs and you can see the current one and move to the next one with , (and the previous one with l). The third one shows this:

‘#+STARTUP:’
     Startup options Org uses when first visiting a file.

     The first set of options deals with the initial visibility of the
     outline tree.  The corresponding variable for global default
     settings is ‘org-startup-folded’ with a default value of
     ‘showeverything’.

     ‘overview’         Top-level headlines only.
     ‘content’          All headlines.
     ‘showall’          No folding on any entry.
     ‘showeverything’   Show even drawer contents.

which is what I linked to above. That takes care of one of your questions. The VISIBILITY values basically mean the same thing, but they modify the global setting (as I showed in the main answer).

In general, the manual is the best source of information, but you have to spend a little time to learn how to navigate in it - btw, to do that, the best way is to read the Info manual! Kill the buffer with the Org mode manual and say C-h i m info RET and spend some time with it. You should also familiarize yourself with the help system: Emacs is self documenting, so you can ask it a whole lot of questions about things - start with C-h ?.