Q:

htaccess point request to sub-directory if file doesn't exists and does under the subdirectory

I'm having a really hard time with trying to get this to work so I have a sub-directory example.com/projects with a directory under that called test and I'd like it if someone typed example.com/test it would show the file from example.com/projects/test but if the file does not exist I would like it to post a 404 error. 
Additionally if possible I would like any time example.com/projects/test was typed it would redirect to example.com/test instead but if someone goes to just projects/ I want them to be able to stay there. 
I have tried the following .htaccess files so far

This works almost perfectly passing through the files unless the file doesn't exist in which it throws a 500 Internal Server Error
RewriteCond %{REQUEST_FILENAME} ! -f
RewriteCond %{REQUEST_FILENAME} ! -d
RewriteRule ^(.*)$ projects/$1 [PT]

I thought something like this might work to only pass through if the file existed under projects but doesn't work at all:
RewriteCond projects/%{REQUEST_FILENAME} -f
RewriteCond projects/%{REQUEST_FILENAME} -d
RewriteRule ^(.*)$ projects/$1 [PT]

For the second part pointing anything that goes to /projects/test to strip /projects I tried this (placed before the code above)
RedirectMatch ^/projects/(.+)$ /$1

Only to find a redirect loop.  How can i prevent this? 

My current .htaccess file for reference:
ErrorDocument 404     /404.html

RewriteEngine On
RewriteCond %{HTTP_HOST} ^www.example.com$ [NC]
RewriteRule ^(.*)$ http://example.com/$1 [R=301,L]
RewriteCond %{HTTP_HOST} ^example2\.com$ [OR]
RewriteCond %{HTTP_HOST} ^www\.example2\.com$
RewriteRule ^/?$ "http\:\/\/example3\.org" [R=301,L]

#RedirectMatch ^/projects/(.+)$ /$1
#RewriteCond %{REQUEST_FILENAME} ! -f
#RewriteCond %{REQUEST_FILENAME} ! -d
#RewriteRule ^(.*)$ projects/$1 [PT]

A:

You can use these rules in your root .htaccess:
DirectoryIndex index.html
RewriteEngine On

RewriteCond %{THE_REQUEST} /projects/(\S+)\sH [NC]
RewriteRule ^ /%1 [L,R=302,NE]

RewriteCond %{DOCUMENT_ROOT}/projects/$1 -f [OR]
RewriteCond %{DOCUMENT_ROOT}/projects/$1 -d
RewriteRule ^(.+)$ projects/$1 [L]

