You are trying to mix mod_rewritewith mod_alias, but statements RewriteCondcannot expose statements Redirectsince they do not come from the same module.
I believe you need something similar if I understood correctly what you are trying to accomplish:
RewriteEngine On
RewriteCond %{REQUEST_URI} !=/events/index.html
RewriteCond %{REQUEST_URI} !=/calendar/index.html
RewriteCond %{REQUEST_URI} !=/info/faq.html
RewriteRule ^.*$ http://mynewsite.com/$0 [R=301,L]
Redirect 301 /info/faq.html http://mynewsite.com/my-page