Yes and yes. I have several "albums' in one account...some, like family photos and such are private and some, like my hobby and blogging stuff are public.
You can upload photos from your PC or email and websites straight to any of your albums, but not from one album to another within the same account (at least not with the free version).
If you had a photo you wanted to move from one album to another, its easy enough to download your own pics back to your computer and then upload them into a separate album though.
I hope this answered your question.