1. I have change my avatar and the old one is still showing.
Just press the "Reload" or "Refresh" button on the browser. It's caching the old one.
2. It always makes me enter my password to make any changes to my account. I noticed that my account here doesn't require me to do that.
It doesn't require you to enter the password to make changes so much as if one of the passwords is provided, the other must be filled in. I think your browser is autofilling the fields. If the page loads with something in either "password" field, clear it out, and it won't require you to enter the info.