Suponho que você deseja redirecionar para HTTPS em todos os casos e o http://
é apenas um erro de digitação.
RewriteCond %{HTTP_HOST} ^oldsite.com [OR]
RewriteCond %{HTTP_HOST} ^www.oldsite.com [NC]
RewriteRule ^/services https://newsite.com/solutions/ [R=301,L]
RewriteCond %{HTTP_HOST} ^oldsite.com [OR]
RewriteCond %{HTTP_HOST} ^www.oldsite.com [NC]
RewriteRule ^/faq/faq1 https://newsite.com/faq/ [R=301,L]
RewriteCond %{HTTP_HOST} ^oldsite.com [OR]
RewriteCond %{HTTP_HOST} ^www.oldsite.com [NC]
RewriteRule .* https://newsite.com/ [R=301,L]