Public Upload into a Picasa Album

You can't, at the moment. Use Picasa on your local computer.

I loved this online feature too, and it's sad that it's gone. However, seeing that the capability appeared only online, and later in the application, I suspect that they removed it from online because it's difficult to merge your face/name assignments from online into your local Picasa installation. It's a lot easier, and more natural, to do the tagging before uploading.

There is nothing you can do besides making them private. If the browser sees the picture the browser can store the picture. This is true for any picture on the internet with the exception of pictures embedded in some sort of flash application but still with a hi res monitor you can get a very nice quality screen shot.

By checking no printing and no download just means that other people can't order prints from picassa or right click save as. ( you can still save using a web inspector ).