WordPress Integration On My Website

I own a custom birthday card company and would like to utilize the word press technology. Is it possible to do the following through the word press technology:

– Enable my customers to have their own birthday party “blog” replicating the design of the card they have chosen.
– The customer’s blog will enable only friends and family who have already attended the birthday party will be able to upload photos, video, and leave comments.(is there a password users can enter in order to view the blog?)
– Have the customer’s birthday party blog web address be my company’s domain followed by the customer’s username. (example: http://www.mycompany.com/username)
– Would users know their blog is offered through word press? I would not like to have the word press name attached to my website, it needs to be a “white label” scenario, because I want to maintain the integrity of my company for marketing and branding purposes.
I would like to know if this is possible with the word press technology, can you please advise on the best way to get started and point me in the right direction. Thank You.