In cygwin I could not modify files in my home directory

Question

In my cygwin terminal, I could not modify files in my home directory

$ echo $HOME
/home/user123

$ cd $HOME

$ pwd
/home/user123

$ ls -ld .
drwxr-xr-x+ 1 user123 None 0 Jan  2 16:46 .

$ touch foo
touch: cannot touch `foo': Permission denied

$ whoami
user123

However, if I Run as administrator when I started the cygwin terminal, I could modify the file

$ echo $HOME
/home/user123

$ cd $HOME

$ pwd
/home/user123

$ touch foo

$ ls -ld foo
-rw-r--r-- 1 user123 None 0 Jan  2 17:00 foo

$ whoami
user123

How can I fix this problem? Thanks!

Update

I checked the folder properties as recorded by Windows, it shows that the check box for "Read-Only" has been checked. (See a screenshot below.) I tried unchecking it but that did not help. Also I noticed two things:

1. The check-box label says "Read-Only (Only applies to files in folder). Does that mean folders are not marked as "Read-Only" not matter what the status of the check box is? Apparently my current problem is that the home folder is marked as read-only (except for Administrator). How do I change that?

2. When I tried to change the "Read-Only" status (unchecked the box and the Apply), I got a lot of pop-up that said

   An error occurred apply attributes to the file Access is denied.

The relevant filepaths are all the files that start with a dot (.) (UNIX hidden files). In my operation, I chose to option of Ignore for these pop-ups

Update 2

The following is the screenshot for the security tab. Note that I the Add button is grayed out (even though I was doing this with Run as administrator). Also, when I entered the tab, there is a pop-up with this message:

The permissions on user123 are incorrectly ordered, 
which may cause some entries to be ineffective.

One more question: how do I know how the two users with long numerical IDs (S-1-5-21-...) are mapped to the symbolic usernames?