I just added an new rewrite rule so I can redirect pages like:
www.Domain.com/PartnerNameHere/
to:
www.Domain.com/LandingPage?page=PartnerNameHere
However now all axd references are not working.
How do I set: ignore extensions for css,jpg,png axd..

Current your match pattern for RewriteUserFriendlyURL1 is ^([^/]+)/?$, which makes no concession for extensions (it's matching any queries with a single URI segment).
If PartnerNameHere can never contain a ., then changing your match pattern to ^([^/.]+)/?$ should be sufficient.
If, however, you only want to block those specific extensions, you'll need to use this: ^(?![^/]+?\.(?:css|png|jpg|axd)$)([^/]+)/?$