D7, static site in root, drupal in subfolder/subdomain

I had to migrate my site to a new server/hosting service (tophost). I set up a subdomain by adding a CNAME record (“blog” on “mysite.ext”), and – as suggested by the registar, I added a .htaccess in the webroot (/htdocs):

RewriteEngine On
RewriteBase / 
#RewriteCond %{HTTP_HOST} blog.mysite.ext
#RewriteCond %{REQUEST_URI} !blog/
#RewriteRule ^(.*)$ /blog/$1 [L]

(* instructions by registar reported tht subdomains have to be handled via .htaccess)
I then uploaded my drupal blog in “blog” subfolder, but I got a 500 server error, alongside other minor problems.

So I had two different .htaccess:
1) [in root, so /htdocs]

RewriteEngine On
RewriteBase / 

RewriteCond %{HTTP_HOST} ^mysite.ext$ [NC]
RewriteRule ^(.*)$ http://www.mysite.ext/$1 [L,R=301]

RewriteCond %{HTTP_HOST} ^blog.mysite.ext$
RewriteRule ^(.*)$ http://www.mysite.ext/blog/$1 [R=301,L]

2) [in drupal folder, so /htdocs/blog] I just kept the .htaccess from local installation, but I uncommented the rewrite base url line and noted /blog

But it doesn’t work: I can access the static site in /htdocs, but when I try and reach the drupal site (/htdocs/blog), by typing blog.mysite.ext or www.mysite.ext/blog, I just keep gettin’ some 500 server error (it says some missing or uncorrect .htaccess file)

Now, my goal is to have
-a main (static) site stored in the root, accessible by typing either www.mysite.ext or just mysite.ext
-a drupal site in the /blog subfolder/subdomain, accessible by blog.mysite.ext and -less important – mysite.ext/blog (and other pages accordingly, e.g. blog.mysite.ext/page or mysite.ext/blog/page).

In order to get this, should I have two different .htaccess or just one? And where I went wrong?
Thank you!

Drupal version: 

Source: https://www.drupal.org/taxonomy/term/37/feed