Remove WordPress logo and login link

Hello,

When i navigate to front page of my site i see the wordpress logo at top left corner and also see login links that upon licking shows wordpress.

For some reason i do not want to show others that i am using WordPress. I want my visitors to register and login from from within my site without knowing wordpress. May i know if this is possible. Which widget i need to show for users to be able to login.

Also is there any widget that allows user to register/login using facebook or any other accounts.

Thanks,
Avinash

[Moderator note: Have you included enough information?]